What is Geometry Used For

Introduction:
Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment- Euclidean geometry- set a standard for many centuries to follow. Here in this topic we are going to see what is geometry used for.

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Uses of geometry:


In home or a building geometry is useful in the improvement of projects. For example, to find the area of the floor, height of a building, to place tiles of particular dimension in a particular area, to place furniture in a required place, estimating the fabric needed, to paint the wall how much paint is needed. Geometry is also used to measure volumes. For example, amount of water needed in the fish tank, volume of the paint the wall by the surface area.

Geometry has many uses to find the size, shape, volume, or position of an object. As a school subject, it helps develop logical reasoning. Architects and engineers use geometry in planning buildings, bridges, and roads. Geometry is used by navigators to guide boats, planes, and even space ships. Military personnel use geometry to guide vessels and aim guns and missiles. Almost everything you do in your daily life involves geometry in some way.

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Some problems in geometry:


1) Find the volume paint used to paint the wall. The paint tin in the form of  a cylinder with radius 12 cm and height 19 cm

Given:                     radius r = 12 cm

                                height h = 19 cm  

Solution:

volume of paint = volume of the cylinder

         Volume of a cylinder  =  `pi` r^2 h

                                                =  3.14 (12)^2 19

                                                = 3.14 (144) 19

                                                = 8591.04 cm^3

Therefore the volume of the pait needed to paint the wall is 8591.04 cm^3.

2) A road roller is cylindrical in shape. The radius of the road roller is 35cm. Its length is 120cm. Find the surface area?

Solution

Given: r = 35cm, h = 120cm.

(i) The surface area = 2`pi` r (h +r)

                                = 2`pi` × 35 ( 120 + 35 )

                                = 34,100 cm2.

Geometry Terms Called Plane

Introduction to geometry terms called plane:

A surface which has thickness as zero and infinitely large in geometry terms is called as plane. The plane is imagined in both direction with infinite large length. In geometry, the plane term is two dimension surface and it does not have edges.This is created from analysis of point, line and space in geometry. Please express your views of this topic Define Parallel Lines by commenting on blog.


Explanation for plane in geometry terms


The terms plane is present in geometry:

In Euclidean geometry, the subspace are used for setting the plane and the plane is called in terms of whole space. The trigonometry, geometry terms are use the plane. The plane is consider the group of points and is called as undefined term.

In geometry the plane is considered as flat surface and the two vectors are used for span the surface. This terms are called linearly independent vectors. The planes are intersected and create the angle is called as dihedral angle.

The nonzero normal vector terms are used to derive the plane equation through the point,

n. ( x – x0 ) = 0 for n = ( a, b ,c ) and X0 = (x0 , y0, z0 )

where X = (x, y, z).This is derive the plane’s general equation as ax + by + cz + d = 0 where d = -ax0 – by0 – cz0.

The distance between the points are calculated as D =  `(d)/(sqrt(a^(2) + b^(2) + c^(2)))` .

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More about plane in geometry


Properties of plane terms in geometry:

In Euclidean space, the parallel planes are present or plane is parallel to the line. Rotation, translation, reflection ans glide reflections are followed in plane motions.

The plane terms in different branches:

A plane which one get the differential structure is called as differential geometry.
The complex analysis is rise the abstraction of complex plane.
If the spherical geometry is taken from a plane means that terms  are called as stereographic projection.

Geometry Terms A Through Z

Introduction to geometry terms a through z

There are number of  terms available in geometry. Learning geometry terms is an essential and an interesting one. The geometry terms are the basis for solving the geometry problems. Without knowing about the geometry terms, we cant able to solve the problems.
The terms of  geometry finds its application also in real life.In this artcle of geometry terms a through z, we are going to learn some of the basic terms involved in geometry.

A through L geometry terms:


Acute angle:  An angle which is greater than 0o but less than 90o is called an acute angle.

Area: The Area of a region is the number of square units that it takes to cover the region.

Angle: An angle is formed by two rays with a common end point called the vertex

Box: A surface which is made up of rectangles.

Collinear Points: If three or more points lie on a line, then the points are called collinear points.

Concurrent lines: If two or more straight lines pass through the same point, then they are called concurrent lines. The point through which the lines pass is known as point of concurrency.

Complementary angles: Two angles are said to be complementary if the sum is equal to 90o

Diameter: A straight line segment that passes through the center of the circle

Equilateral triangle: The triangle having all the sides are equal.

Hexagon : A six sided polygon

Hypotenuse: The side opposite to the right angle in a right triangle.

Intersecting planes: The planes which share a line is referred as Intersecting planes.

Kite: Kite is a quadrilateral which has two distinct pairs of consecutive equilateral side.

Locus: Locus is a set that satisfies the given condition.


M through Z geometry terms:


Mean: The average for the set of given data's.

Mid-Range: The arithmetic mean of maximum value and minimum value given in a data set

Null set: An empty set is called as null set.

Obtuse Angle: An angle which is greater than 90o but less than 180o is called an obtuse angle

Plane: A plane is a set of points on a flat surface that extends without end in all directions.

Parallel lines: The lines that lie in the same plane and never intersect are called as Parallel lines.

Perpendicular lines: If two lines lie in the same plane and intersect at right angles, they are called perpendicular lines.

Quadrilateral: Afour sided polygon such as square,rectangle etc.

Ray: A ray starts from a fixed point and extends endlessly in one direction.

Right Angle: An angle of measure 90o is called a right angle

Straight Angle:An angle of measure 180o is called a straight angle.

Supplementary Angle: The two angles are said to be Supplementary if the sum is equal to180o

Surface Area: The total area of the surface of a solid object

Trapezium: A quadrilateral in which two opposite sides are parallel and two opposite sides are non-parallel

Vertical angles: The angles which share a common vertex and whose sides form two lines

Zero dimensional: The object having no dimension.

Geometry Determining an Angle

Introduction:

In mathematics, an angle is the branch of geometry which is defined as the two rays sharing a common endpoint to form the figure is the vertex of the angle. The amount of rotation is the magnitude of the angle that separates the two rays. For the geometric configuration and its angular magnitude the term "angle" is used. The word angle means "a corner" which is come from Latin. There are different types of angle in geometry.They are Right angle, Straight angles, acute angles, Obtuse angles, Complementary angle, Supplementary angles.


Conditions for determining an angle:


Let as assume the x be the variable for angle. Then,

Right angle

Right angle is the angle in which the value of angle is 90 degree.

If x = 90 degree, it is right angle.

Straight angle

Straight angle has the angle value as 0 degree.

If x = 0 degree, it is straight angle.

Acute angle

When the angle value is below 90 degree then it is acute angle.

If 0 < x < 90 degree, it is acute angle.

Obtuse angle

When the angle value is above 90 degree then it is obtuse angle

If x > 90 degree, it is obtuse angle.

Let as assume x and y are two angles. Then,

Complementary angle

The angles are called as complementary angle when the sum of the two angles is 90 degrees.

If x + y = 90 degree, it is Complementary angle.

Supplementary angle

The angles are called as Supplementary angle when the sum of the two angles is 180 degrees.

If x + y = 180 degree, it is Supplementary angle.

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Examples:


Example 1: find the type of angle for below values?

1. x = 10
2. x = 90
3. x = 300
Solution:

1.  The given value is x = 10 degree.

It satisfy the condition 0 < x < 90.

Therefore, it is an acute angle

2. The given value is x = 90 degree.

It satisfy the condition x = 90.

Therefore, it is right angle.

3. The given value is x = 300 degree.

It satisfy the condition x > 90.

Therefore, it is an obtuse angle

Example 2: Check whether the angles are Complementary angle or Supplementary angles for given data below?

1. x = 30, y = 60

2. x = 80, y = 100

Solution:

1. x = 30, y = 60

x + y = 30 + 60

= 90

Therefore, it is Complementary angle.

2. x = 80, y = 100

x + y = 80 + 100

= 180

Therefore, it is Supplementary angle.

Area of a Kite Geometry

Introduction about kite in geometry:

In geometry a kite, or deltoids, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the sides of equal length are opposite. The two diagonals of a kite are perpendicular and half the product of their lengths is the area of a kite. It has four vertices's. We can calculate the area for many shapes in geometry. In this article we shall discus about how to how to calculate area of kite with geometry example problems.

Source-Wikipedia

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Geometry Formula and example problems:

The space occupied by the kite is called area of kite.

Formula:

Area of kite (A) = half the product of two diagonals.

Let assume,

d1 and d2 are the two diagonal of kite.

Area of kite (A) = (d1 x d2) /2 square unit.

Example problems:

1. Find the area of kite whose diagonal length diagonal (d1) = 20cm and diagonal (d2) = 15cm.

Solution:

Given:

Diagonal (d1) = 20cm

Diagonal (d2) = 15cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (20 x 15) / 2

= 100/2

=50

Area of kite (A) = 50 cm^2

2. Find the area of kite whose diagonal length diagonal (d1) = 12cm and diagonal (d2) = 8cm.

Solution:

Given:

Diagonal (d1) = 12cm

Diagonal (d2) = 8cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (12 x 8) / 2

= 96/2

=48

Area of kite (A) = 48 cm^2

3. Find the area of kite whose diagonal length diagonal (d1) = 25cm and diagonal (d2) = 15cm.

Solution:

Given:

Diagonal (d1) = 25cm

Diagonal (d2) = 15cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (25 x 15) / 2

= 375/2

=187.5

Area of kite (A) = 187.5 cm^2

4. Find the area of kite whose diagonal length diagonal (d1) = 8cm and diagonal (d2) = 6cm.

Solution:

Given:

Diagonal (d1) = 8cm

Diagonal (d2) = 6cm

Formula:

Area of kite (A) = (d1 x d2) / 2

= (8 x 6) / 2

= 48/2

=24

Area of kite (A) = 24 cm^2

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Area of kite geometry – practice problem:


1.      Find the area of kite whose diagonal length diagonal (d1) = 12cm and diagonal (d2) = 6cm.

Answer: Area (A) = 36cm^2

2.      Find the area of kite whose diagonal length diagonal (d1) = 18cm and diagonal (d2) = 9 cm.

Answer: Area (A) = 81 cm^2

3.      Find the area of kite whose diagonal length diagonal (d1) = 8cm and diagonal (d2) = 6cm.

Answer: Area (A) = 24 cm^2

What is a Pentagon in Geometry

Introduction to Pentagon in geometry:

Pentagon is the one of the important mathematical figure in geometry.  It is a five sided polygon.  Pentagon is making with the help of 5 sides and 5 angles. Pentagon is classified into following two types.  They are

Regular Pentagon
Irregular pentagon
In this article we have to study about what is pentagon in geometry.


Brief Study about what is a pentagon in geometry?


What is Regular pentagon in geometry?

A pentagon is usually 5 sided figures.  The sides and angles are equal of the pentagon are equal in measure so it is named as regular pentagon.

What is Irregular pentagon in geometry?

Irregular pentagon is also one of the types of pentagon.  Here the sides and angles are not equal in measure.  They are different sides and angles.  So it is named as irregular pentagon.

What is the Pictorial representation of the Regular Pentagon?

What are the Properties of the regular pentagon?

5 sides are equal in measure
5 angles are equal in measure.
Sum of the interior angles measures 540 degree
Each interior angle measures 108 degree
Sum of the exterior angles measures 360 degree
Exterior angle measures 72 degree
Pentagon is formed with the help of three triangles
Pentagon has five lines of reflectional symmetry
Pentagon has five lines of rotational symmetry

What is the area of the regular and irregular pentagon?

The following formula is used to find the area of the regular pentagon,

A=`(1)/(2)` x Apothem X Perimeter

Here A is the area of the pentagon

Apothegm is the radius of the in circle of the pentagon

Perimeter is the sum of all sides of the pentagon

This is the formula to calculate the area of the pentagon.

Geometry Proportions

Introduction of geometry proportions:-

In mathematics, Proportions in arithmetic and geometry, a particular relation between groups of numbers or quantities. In arithmetic, proportions are the equality of ratios; ratio is the division of one number by another. A continued proportions is a property of every three terms in a geometric progression. A proportions is a statement that two ratios are equal such as a:b = c:d.



Example problem for geometry proportions:-


Problem1:

Are the ratios 30g: 40g and 48 kg: 72 kg in geometry proportions?

Solution:

30 g: 40 g =30 / 40 = 3 / 4

= 3: 4

48 kg: 72 kg = 48 / 72 = 4 / 6

= 4: 6           So, 30: 40 = 48: 72.

Therefore, the ratios 30 g: 40 g and 48 kg: 72 kg are in geometry proportions,

i.e. 30 : 40 :: 48 : 72.

The middle terms in this are 40, 48 and the extreme terms are 30, 72.


Problem 2:

Do the ratios 30 cm to 4 m and 20 sec to 5 minutes form a geometry proportions?

Solution:

Ratio of 30 cm to 4 m = 30: 4 × 100 (1 m = 100 cm)

= 3: 40

Ratio of 20 sec to 5 min = 20: 5 × 60 (1 min = 60 sec)

= 20: 300

= 1:15

Since, 3: 40 ≠ 1: 15, therefore, the given ratios do not form a geometry proportions.



Problem 3:

Sam works as a dental hygienist. Last week Sam ade 500 for 20 hours of work How many hours must Sam work in order to make 800?

Solution:

Sam works as a dental hygienist

50020hours=800 / x hours

20 hours * $800 = x hours * $500

16000 = $500 x

16000 / 500 = x

32 = x

Sam 32 hours work in order to make $800

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Practice problems for Geometry proportions problems:        


Problem 1:

Gabriella bought five cantaloupes for 3 How many can taloupes can Shayna buy if she has21?

Answer: 35 gabriella

Problem 2:

If you can buy one can of pineapple chunks for 5 then how many can you buy with 10 ?

Answer: 50 pineapple chunks

Problem 3:

If you can buy four bulbs of elephant garlic for 12 then how many can you buy with 96?

Answer:  8 bulbs

Problem 4:

One package of blueberries costs 6 How many packages of blueberries can you buy for 42?

Answer: 7 blueberries

Geometry Sample Test

Introduction to Geometry sample test:

Geometry is the method  of finding  the volume or  dimension of an object. Buildings, cars are some examples of geometry. Geometry sample test help students in finding the area, perimeter, circumference of  Two-dimensional figures like triangle, circle, rectangle, rhombus, trapezoid, quadrilateral etc.Geometry  sample test problems are used in real life situations such as how much water can we store in a tank. Here lot of geometry sample test questions are given with answers for our practice.


Geometry sample test:


Example 1:

Find the perimeter of square whose sides are 17 cm.

Solution:

given the side if square is 17 cm

Perimeter of the square, P = 4a

= 4 × 17 cm

=  68 cm

Hence the perimeter of square is 68 cm.

Example 2:

Find the volume of right cylinder that has radius 5 cm and height 12 cm.

Solution:

Given, r = 5 cm

h= 12 cm

Volume of circular cylinder = pi * r2 * h cu. Units

= `(22/7)` * 5 * 5 * 12 = 942

Volume of circular cylinder = 942 cm^2

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Geometry sample test:


Example 3:

The perimeter of the floor of a square room is 35m. Find the area of the floor of given perimeter.

Solution :

To find the area of a given square of perimeter 35 m, we need to measure its side. Here perimeter of the square is given, we
need to find the side of square from its perimeter.

Perimeter of square ground, p = 4a

4a = p

a = p/4

Hence, a = 35 / 4 m [since p = 22 m ]

∴ a = 8.75 m

Area of the square ground A = a2

= 8.75 m × 8.75 m

i.e. Area = 76.5625 sq.m.

Example 4:

Find the volume of the right prism whose area of the base is 450 cm^2 and height is 28cm

Solution:

Given that area of the base, A = 540 cm^2 and height (h) of the prism = 13 cm

Volume of the right prism = area of the base * height cu.units

= A * h

= 540⋅13

Volume of right prism = 7020 cm3

Geometry Parallelograms

Introduction for geometry parallelograms:

In geometry, parallelogram is a shape that has four sides where the opposite sides are parallel to each other. The main concepts of the parallelograms are,

The opposite angles are equal

The opposite sides are equal in its length and are parallel to each other.

Now we are going to see about the geometry - parallelograms and its problems.


Problems for geometry parallelograms:

Example 1:

Find the sides of the parallelogram having 10 cm which is the smaller side of the parallelogram. The longest side is 3 times the smallest side of the parallelogram.

Solution:

The smallest side of a non regular parallelogram = 10 cm (known)

The longest side of the parallelogram will be 10 × 3 = 30 cm.

This is due the opposite sides are equal in the parallelograms

Thus the other two sides are 10 cm and 30 cm respectively.

The irregular quadrilaterals sides, parallelograms = 10 + 30 + 10 + 30 = 80 cm.

Example 2:

Determine the sides of the parallelogram having 15 cm which is the smaller side of the parallelogram. The longest side is 5 times the smallest side of the parallelogram.

Solution:

The smallest side of a non regular parallelogram = 15 cm (known)

The longest side of the parallelogram will be 15 × 5 = 75 cm.

This is due the opposite sides are equal in the parallelograms

Thus the other two sides are 15 cm and 75 cm respectively.

The irregular quadrilaterals sides, parallelograms = 15 + 75 + 15 + 75 = 180 cm.

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More problems for geometry parallelograms:


Example:

Determine the area of parallelogram where the base and height of the parallelogram are 12 cm and 20.

Solution:

Given data is the base, b =12 cm and the height, h =20 cm

We know the formula for the area of parallelogram and given as,

Area of the parallelogram = b × h

Substitute the value of b and h,

Area of parallelogram = 12 × 20

= 240 cm^2

Therefore the area of a parallelogram is 240 cm^2

Geometry Concurrent Lines

Introduction to Geometry concurrent lines

Concurrence
Definition Of concurrent lines
Examples of concurrent lines
Concurrence in Triangle
Concurrence in Circle
Concurrence

The phenomenon when  multiple lines meet at a point is known as concurrence.


When two or more  lines in a plane intersect at a common point then they are said to be concurrent lines.

Examples of geometry concurrent lines

Altitudes of a triangle are concurrent lines
Angular bisector of a triangle are concurrent lines
Perpendicular bisectors of a triangle are concurrent lines
The medians of a triangle are concurrent lines
The diameters of a circle are concurrent lines

Geometry concurrent lines in a triangle


Incenter is the point of concurrence of the angular bisector of a triangle , therefore  the angular bisectors of a triangle are concurrent lines. Angular bisectors are the lines which divide each angle of a triangle in two equal angles they meet at in center.
Circumcenter is  the point of concurrence of perpendicular bisectors of a triangle, therefore perpendicular bisectors of a triangle are concurrent lines. Perpendicular bisectors of a triangle are the lines which divide each side in two equal parts they meet at the circumcenter .


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Orthocenter  is the point of concurrence of altitudes of a triangle, therefore  altitudes of a triangle are concurrent lines. Altitudes are the perpendicular from each vertex of a triangle to the opposite sides, they meet at the ortho center.
Centroid is the point of concurrence of medians of a triangle , therefore medians of a triangle are concurrent lines. Medians are the lines joining the vertex to the mid point of opposite sides, they meet at centroid.
Geometry concurrent lines in a circle.

Center of a circle is the point of concurrence of all the diameter, therefore all the diameters of a circle are concurrent lines . Diameter of a circle is the line joining  two points on the circumference passing through the center .

Three Different Types of Geometry

Introduction:

A non-Euclidean geometry is learning of figures and structure that do not chart straight to any n-dimensional Euclidean system, describe by a non-vanishing Riemann curve tensor. Examples of non-Euclidean geometries contain the hyperbolic and elliptic geometry, which are difference with a Euclidean geometry. The necessary difference among Euclidean and non-Euclidean geometry is the character of parallel lines.


Behavior of lines


Three different types of geometry method to explain the difference connecting these geometries is to think double directly lines indefinitely extensive in a two-dimensional level surface that are together vertical to a three line types:

In Euclidean geometry the position remain at a stable distance starting each other, and are well-known as parallels.
In hyperbolic geometry they "curve away" starting each other, rising in distance as one moves further from the position of intersection through the general perpendicular; these lines are frequently called ultra parallels.
In elliptic geometry the positions “curve toward" each extra and finally intersect.


Models of non-Euclidean geometry


Let us see about three different types of  geometry,

Elliptic geometry

The simplest type for elliptic geometry is a globe, anywhere lines are "great circles" (such as the equator or the meridians on a globe, and points reverse each other are recognized (considered to be the equal).In the elliptic type, for some certain line l and a point A, which is not on l, all position throughout A will intersect l.

Hyperbolic geometry

The pseudo globe has the suitable curve to model a section of hyperbolic space, and in a second document in the similar year, defined the Klein model, the Poincaré disk type, and the Poincaré half-plane type which type the total of hyperbolic space, and old this to explain three different types of geometry that Euclidean geometry and hyperbolic geometry be equip reliable, so that hyperbolic geometry was reasonably constant if and simply if Euclidean geometry.


Their Relationship to Each Other


Let us see about three different types of  geometry,

The different geometries are divided and connected to single another in different ways. The non-Euclidean geometries are closely similar to the geometry of Euclid, but that Euclid's postulate concerning analogous lines is replace and all theorems depending on this assume are changed therefore both Euclidean and non-Euclidean geometry are models of metric geometry, in which the length of line division and the volume of position may be careful and compared.

Why is Geometry Important

Introduction :

Geometry is a study of relationship between size and shapes. It was a fully study of angles, shape of objects, area of an object and volume of an object and perimeter. Geometry was fully originated two-dimensional and three dimensional objects. In every day geometry is nearly a rounded me .Without geometry we cannot identify the shape of an objects and also properties of an object. Why geometry important means ,Mainly when and how we have to apply the relationship and measurement of angles ,shapes,lines,solids and surface areas for the better preparation.


Why is geometry important in reallife:


Geometry used in technology

Computer graphics
Structural engineering
Robotics technology
Machine imaging
Animations applications
General application for geometry:

For example we having rectangular garden, now we have to find the area of the grassed rectangular space mean, we use for measuring tools for finding measurement height, length of the garden and then easily find the area of garden using geometry concepts.

Why geometry important:

Used to identifying the shape and size of an object.
Finding the area, volume, Surface area of an object and also we have to know about angles, lines. Properties of an object.
Use more technologies for  finding the transformation  and position of an objects from the original condition.


Why geometry is important in technologies:


Computer graphics: Computer graphics is fully based on geometry concepts. Why geometry was important in computer graphics mean, How the objects or images are transferred from one position to another position and also changes in that position.

Robotics technology:  In robotics technology geometry was using mean, how to grasp a objects shape, also how to move the shape without collision.

Computer-aided design:  Geometry is also used computer aided geometry design. It was represented to create or make the objects based how the user instruct to the machines. Example making a car.

Solving Geometry Practice

Introduction for geometry:

Geometry is one of the main branch of mathematics. The  word  “geometry”  is resultant from the combination of two Greek words “geo” and “metron”.  geo means “earth” and metron  means “measurement”. ”Euclid, a distinguished Greek mathematician, called the father of geometry. A point is used to represent a place in space. a plane to be a surface extending infinitely in all directions such that all points lying on the line joining any two points on the surface.


Example problems for geometry:


Example 1:

Solving the following equation, Calculate the values for x-intercept, the y-intercept, and the slope .

2x + 4y = 20

Solution:

The slope intercept form, y= mx +b

Here   m represent slope

b represent y intercept

2x+4y=20

On solving this, We get

4y = 20-2x

4y = -2x+20

On solving this, We get

y = (-2/4) x+20/4

y = (-1/2) x+5

X-intercept = 5

Y-intercept = 5

Slope = - 0.5

Example 2:

John wants to decorate her Christmas tree. He wants to place the tree on a greeting box covered with colored paper with picture of Santa Claus on it. He must know the correct quantity of paper buying for this purpose. If the box has length, breadth and height as 60 cm, 20 cm and 10 cm respectively how many square sheets of paper of side 10 cm would he need?

Solution:

Since John wants to paste the paper on the outer surface of the box, the quantity of paper required would be equal to the surface area of the box, which is of the shape of cuboids. The dimensions of the box are:

Length =60 cm, Breadth = 20 cm, Height = 10 cm.

The surface area of the box = 2( lb + bh + hl )

= 2[(60 × 20) + (20 × 10) + (10 × 60)] cm^2

On solving this, We get

= 2(1200 + 200 + 600) cm^2

= 2 × 2000 cm^2 = 4000 cm^2

The area of each sheet of the paper  = 10 × 10 cm^2

= 1000 cm^2

Therefore,    the required sheet  = surface area of box/ area of one sheet of paper

= 4000/1000

On solving this, We get

= 4

Therefore, he would need for 4 sheets.

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Practice problems for geometry:


Practice problem 1: Determine the slope of the line whose equation is 3x + 4y = 12 and whose y-intercept is (0,5)

Ans: m = -3/4

Practice problem 2: The two angle is 40° , 56° ,  Find the third angle of triangle.

Ans: 84°

Practice problem 3:  What is the complementary  angle of 39°

Ans: 51°

Practice problem 4: Find the slope  of the line whose equation is 3x + 4y + 5 = 0.

Ans: m = - 3/4 , c = -5/4

Geometry Tools Online

Introduction for geometry tools online:

Geometry tools online describes how to handle the geometry tools and its measurement uses. Geometry tools online such as protractor, divider, and compass which are complicated to measure and to draw. For that, we have to know some basic geometry knowledge and angles determination. Geometry tools online explains use and methods to measure.
A Geometrical instruments box contains a whole geometric tools and basic requirement for those who learn geometry.

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Geometric tools online and its measure techniques are as follows:


Ruler:
Ruler is used to measure the length of line segment .Ruler has one edge is graduated in centimeters and the other edges with inches. A ruler is used to draw neat lines and to measure the length of the line segment.

Compass:
Compass is used to draw a circle with a given measurement of its radius and a line segment. We can also construct the angles for given measures with the help of compass. There is a provision given for compass to insert a pencil.

Divider:
It is used to measure the length of a line segment and to compare the lengths of two given line segments.

A pair of Set – Squares:
They are used to construct perpendicular lines and parallel lines. One set-square has 30° - 60° - 90° angles at the vertices and the other has 45° - 45° - 90° angles at the vertices.

Protractor:
A protractor’s curved edge is graduated into 180 equal parts. Each line part is equal to one degree.The semi circle line graduation starts from 0° on right hand side and ends with 180° on left hand side and vice versa. A protractor is used to construct and to measure given angles.

To construct almost accurate figures remember the following :

In the instruments box all the instruments should have fine edges and tips.
It is better to have an eraser and two pencils in the box, so as to use one pencil with compass for inserting in it and the other to draw lines and mark points.
Always draw thin lines and mark points lightly.

Minutes in Geometry

There are several ways to measure the size of an angle. One way is to use units of degrees. (Radian measure is another way.) In a complete circle there are three hundred and sixty degrees.

An angle could have a measurement of 35.75 degrees. That is, the size of the angle in this case would be thirty-five full degrees plus seventy-five hundredths, or three fourths, of an additional degree. Notice that here we are expressing the measurement as a decimal number. Using decimal numbers like this one can express angles to any precision - to hundredths of a degree, to thousandths of a degree, and so on.

There is another way to state the size of an angle, one that subdivides a degree using a system different than the decimal number example given above. The degree is divided into sixty parts called minutes. These minutes are further divided into sixty parts called seconds. The words minute and second used in this context have no immediate connection to how those words are usually used as amounts of time.


Symbols used


In a full circle there are 360 degrees. Each degree is split up into 60 parts, each part being 1/60 of a degree.  These parts are called minutes. Each minute is split up into 60 parts, each part being 1/60 of a minute. These parts are called seconds.

There are symbols that are used when stating angles using degrees, minutes, and seconds. Those symbols are show in the following table.
Symbol for degree:  º
Symbol for minute:   '
Symbol for second:  "

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Example


So, the angle of 40 degrees, 20 minutes, 50 seconds is usually written this way:

How could you state the above as an angle using common decimal notation? The angle would be this many degrees, (* means times.):
40 + (20 * 1/60) + (50 * 1/60 * 1/60)

That is, we have 40 full degrees, 20 minutes - each 1/60 of a degree, and 50 seconds - each 1/60 of 1/60 of a degree.

Work that out and you will get a decimal number of degrees.  It's 40.34722 º

Geometry in Our World

Introduction to geometry in our world

Geometry is one of those subjects that make students wonder when they will ever use it again. Yet, it has many applications in daily life in our world.


Geometry is especially useful in home building or improvement projects. If you want to find the floor area of a house, you use geometry. This information is useful for laying carpet or tiles and for telling an estate agent how big your house is when you want to put it on the market. If you want to reupholster a piece of furniture, you have to estimate the amount of fabric you need by calculating the surface area of the furniture.

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Applications of geometry in our world


Geometry also has applications in our world in hobbies.  The water in a goldfish tank needs to have a certain volume as well as surface area in order for the fish to thrive. You can calculate it using geometry. Pastimes like quilting and other design projects use geometry extensively. Understanding how the shapes of a quilt block fit together is dependent on geometry; so is determining the amount of fabric you need.

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Geometry in daily life in our world


Geometry plays an important role in every day life. For example, geometry is used in the planning and making of buildings, roads, bridges and houses. Geometrical tools are utilized in making maps and it aids a lot in exploring distances. Geometry is mostly used in drawings, sewing,mathematics,architecture, measurements and so on. It is also used in space, engineering, fashion designing etc.

One  biggest use of geometry is for coordinate transformation (rectangular to polar or vice versa). Many of the applications  you mention make more use of rules of thumb and/or formulas or tables that have been worked out on the basis of geometry. The underlying geometry may be used only rarely.

USE OF GEOMETRY IN DAILY LIFE

Geometry is the one of the subject that make students wonder when they will ever use it again .yet; it has many applications in daily life.

Geometry is especially used in home building or improvement projects .if you want to find the floor area of a house, you can use geometry. These information is useful for telling an estate , how big your house is when you want to put it on the market .if you want to purchase a piece of wood ,you have to estimate the amount of varshines you need the calculating the surface area of the wood.


Importance of study of geometry


Geometry is considered the important field of study, because it has many applications in daily life .for example, a sport car move in a circular path and it applies the concepts of geometry. Stairs are made in the homes in consideration to angle of geometer and stairs and designed to 90 degree. When you throw a round ball in a round basket ball, it is also an application of geometry .Moreover, geometry is widely used the field of many ways such as architecture, decorators, engineers etc. In the architecture for building design and map marking, in addition, geometrical shapes are circle, rectangle, polygon, square, are used in the artists. The most interesting example is the nature of speaks of geometry and you can shapes in all things or nature.

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In daily life there is a lot of use of geometry by Architects, Decorates,

Engineers and many other professionals in determining distances, volume, angles , areas etc and it helps in understanding the proportion of thing in the universe. There is a wide use of geometry in textile and fashion designing and countless other areas.

Geometry is used because we need to help us the house hold tasks like putting carpet in the room ,if you need to know that the shape of the room is and then you need to know the area formula for that the shape so therefore it  is used in the way.

Geometry is at work everywhere you go. Without geometry, we would not be able to build things, manufacture things or play sports with must success. Geometry not only makes in every day life possible, it makes them easier by providing us with an exact science to calculate measurement of shape.

Geometry Theorem List

Geometry is the study of shapes and configurations. It attempt to understand and classify spaces in various mathematical contexts. For a space with lot of symmetries the study naturally focuses on properties which are invariant (remaining the same) under the symmetries. Other type of geometry-In general, any mathematical construction which has a notion of curvature falls under the study of geometry.

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Examples of Geometry Theorem List


Differential geometry: which is the  natural extension of calculus and linear algebra and is known simplest form of vector calculus
Algebraic geometry: This studies objects defined by polynomial equations. This is vital to recent solution is  many difficult problem in number theory, such as the finiteness of solutions to the polynomial equations considered in Fermat's Last Theorem.
Semi-Riemannian geometry: which Einstein is used to study the four dimensional geometry of space and time.
Simplistic geometry: which originated with the study of the evolution of simple mechanical systems, but now pervades all aspects of theoretical physics.



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Lines of Geometry Theorem List


Lines  A line is one of the basic terms in geometry. We may think of a line is a "straight" line that we might draw with a ruler on a piece of paper, except that in geometry, a line extends forever in both directions. We write the name of  line  is passing through two different points A and B as "line AB" or as the two-headed arrow over AB signifying a line passing through points A and B. Points-A point is one of the basic terms in geometry. We may think of a point as a "dot" on a piece of paper. We identify this point with a number or letter. A point has no length or width. It just specifies an exact location. Intersection The term intersect is used when lines, rays, line segments or figures meet, that is, they share a common point. The point they share is called the point of intersection. We say that these figures intersect.

Solving Geometry Examples

Introduction of solving geometry examples:-

In geometry, we deal with the problems in triangles, circle, and square are solved using certain formulas is called Solving geometry examples. Here the formulas are very important to solve any examples problems. From this we can find area, volume, and perimeter etc.

To solving the geometry examples are,

Area of triangle formula =½(bh)

Area of square formula = a²

Area of circle formula = πr²

Area of rectangle formula = l*b


Examples for solving Geometry Problems


Example 1:

Find the area of square given that a= 35?

Solution:

Area of square = a²

= 35²  (calculate the area square )

= 1225

Area of square =1225

Example 2:

Find the area of triangle given that base = 21, height = 18?

Solution:

Area of triangle = ½(bh)

= ½(21*18) ( multiply the values)

= ½(378)

= 189

Area of triangle = 189

Example 3:

Find the area circle given that diameter = 26?

Solution:

Area of circle = πr²

But the radius is not given here; we have found the radius from diameter.

Radius = diameter /2

Radius = 26/2 ( dived the values)

Radius = 13

Area of circle = πr²

Area of circle = π*13²

=3.14*169 ( multiply the values)

Area of circle = 530.66sq.m.

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Examples for solving Geometry Problems


Example 4:

Find the length of the rectangle given that area = 155 and base = 23?

Solution:

Area of rectangle = l*b

155 = l*23

l= 155/23

l = 6.7

l = 7

Example 5:

Find the dimension of 3rd side. When the perimeter is fifty and the two sides are same. The equal sides have five greater the 3rd side?

Solution:

Let us assume s be the unknown length of the triangle, then

We know that perimeter of triangle is

P = a+b+c

50 = s + s + s+ 5

50 = 3s + 5

Then solving  the value of variable s, we get
3s = 50 – 5
3s = 45
s =15

The value of third side = 15 + 5 =20

The value of the third side is 20

Solve Online Geometry Problems

Introduction to solve geometry problems online:

Geometry is one of the important topics in math which includes the study of all kinds of shapes and their properties. Points is one of the basics of geometry. There is no length, height or width.  Points have  four main properties that is exact location, dot, node and ordered pair. Geometry deals with plane geometry, solid geometry. Let us see about solve online geometry word problems.


Solve the geometry word problems online


Q 1: A triangle has a perimeter of 78. If 2 of its sides are equal and the third side is 6 more than the equal sides, what is the length of the third side?

Sol:

Step 1: Let us take Y is the length of the equal sides of triangle

So, the third side of the triangle is Y+6

Step 2:  Perimeter is derived by sum of three sides on triangle.

Step 3: To Plug in the values of above problems.

78= Y+Y+(Y + 6)

Then Combine the similar terms
78 = 3y + 6

3y = 78 – 6
3y = 72
y =24

That is the third side is 6 more than the equal sides.

So, the length of third side = 24 + 6 =30

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More examples to solve geometry word problems online


Q 2 : The perimeter of a rectangle is 1000 meters and its length L is 6 times its width W. Find W and L, and the area of the rectangle.

Sol:

Step 1: Using formula for perimeter of the rectangle.

2 L + 2 W = 1000 ----------- (1)

Step 2: Here the length (L) of rectangle is 6 times more than its width (W)

L = 6 W --------------------- (2)

Step 3: To plug L value in the equation (1).

2(6 W) + 2 W = 1000

Step 4: 12W+W=1000
14 W = 1000

Step 5: Now Find the value of W.

W = 1000 / 14

W = 71.42 meters

Step 6: To plug W value in to equation (2)
L = 6 W

= 6 * 71.42 meters

= 428.57 meters

Step 7:  Area of a rectangle = L * W

L * W = 428.57 * 71.42

= 30608.57 meters 2.