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.

Solving Geometry Homework

Geometry:

Geometry is the main branches of mathematics. The geometry different types of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. The word ‘Geometry’ means learn of properties of figures and shapes and the relationship between them. A system of geometry is called Euclidean geometry. A solid geometry classified to a set of problems or objects.

(Source-Wikipedia)


Solving homework 1:


To calculate the area of a cylinder given that its radius is 8 and its length or height is 6.

Solution:

The surface area of this cylinder is 2 `pi` RL+2 `pi` R2.

= 2*3.14*8*6+2*3.14*82=703.717

The surface are of a cylinder is 703.717

Solving homework 2:

To calculate the perimeter of a rectangle given that its width is 7 and its height is 6.

Solution:

The perimeter is the distance around the rectangle, or h+w+h+w or 2h+2w.

Perimeter = 2 * 6 + 2 * 7 = 26

The perimeter of rectangle is 26


Solving homework 3:


To calculate the area of a rectangle given that its width is 8 and its height is 7.

Solution:

The area enclosed by rectangle, is h × w

Area = 7 * 8 = 56

The area of a rectangle is 56

Solving homework 4:

To calculate the area of a right triangle given that its base is 10 and its height is 8.

Solution:

The area of a right triangle is 1/2bh

Area = ½ * 10 * 8 = 40

The area of a rectangle is 56

Solving homework 5:

To calculate the side of a square given that its area is 8.

Solution:

The area is the amount of space enclosed by the square is S × S or Area=S2.

Solve this equation for S to get that or S=Area1/2 Side = area ½=81/2=2.82843

The side of this square has a length of 2.82843

Solving homework 6:

To calculate the area of  rhombus whose diagonal lengths are  8 and 12.

Solution:

The area of the rhombus= 1/2  x length of the diagonal 1 x length of the diagonal 2 .

=1/2 x 8 x 12

The area of the rhombus = 48