Solving Geometry Perimeters

solving geometry perimeters:

Geometry is the study of all kinds of shapes and their properties.

Plane geometry  is the study of two dimensional shapes such as lines, circles, triangles etc.

Solid geometry is the study of three dimensional shapes like polygons, prisms, pyramids, sphere, cylinder, cone etc.

Perimeter is defined as the total distance around the outside of a 2D shape. Perimeter can be calculated by adding all the lengths along the periphery of a shape.

Let us see solving geometry perimeters in this article


Solving Geometry Perimeter


The Perimeter of rectangle P is the Addition of two times length l and two times width w.

Formula:           P = 2 * length + 2 * width

Example:

Find the Perimeter of rectangle for the length is 6 cm and Width is 5 cm.

Solution:

Perimeter of the rectangle          P =  2 * 6  + 2 * 5

P = 12 + 10

P = 22 cm. Answer.

Perimeter of square:

The Perimeter of any square P is the product of 4 and a side.

Formula:                P = 4 * side

Example:

Find the Perimeter of square for the side is 4 cm.

Solution:

Perimeter of the square A = 4 * 4

A = 16 cm. Answer.

Having problem with Surface Area of a Prism keep reading my upcoming posts, i will try to help you.

Solving Geometry Perimeter for parallelogram and triangle


Perimeter of Parallelogram:

The Perimeter of any Parallelogram is the addition of 2 times side a and 2 times side b.

Formula:           P = 2 * side a + 2 * side b

Example:

Find the Perimeter of Parallelogram for the side a is 7 and side b is 9 and height is 5.

Solution:

Perimeter of Parallelogram        P = 2 * 7 + 2 * 9

P = 14 + 18

P = 32 . Answer.

Perimeter of Triangle:

The Perimeter of Triangle P is the Addition of all the three sides.

Formula:           P = AB + BC + AC for triangle ABC

Example:

Find the Perimeter of triangle for the AB = 7 cm , BC = 5 cm and AC = 7 cm.

Solution:

Perimeter of the triangle            P =  7 + 5 + 7

P = 19 cm. Answer.

Solving Geometry Problems Online

Introduction to solving geometry problems online:

Geometry is a part of math which involves the study of shapes, lines, angles, dimensions, etc. it plays vital role real time application like elevation, projection. Learning geometry provides many foundational skills and helps to build the thinking skills of logic, deductive reasoning, and analytical reasoning. Flat shapes like lines, circles and triangles are called the Plane Geometry. Solid (3-dimensional) shapes like spheres and cubes are called Solid geometry. In this article we shall discuss about solving geometry problems online.

I like to share this Surface Area of a Hemisphere Formula with you all through my article.

Sample problems for online geometry solving:


Example 1:

The perimeter of a rectangle is 800 meters and its length L is 3 times its width W. Find W and L, and the area of the rectangle.

Solution:

Perimeter of rectangle=2L+2W,

2 L + 2 W = 800

We now rewrite the statement. Its length L is 3 times its width into a mathematical equation as follows:

L = 3 W

We have to substitute L =3W in the equation 2 L + 2 W = 800

2(3 W) + 2 W = 800

8 W = 800

W =100 meters

Use the equation L = 3 W to find L.

L = 3 W = 225 meters

Use the formula of the area.

Area = L x W = 225 * 100 = 22500 meters 2.

So, the area of the rectangle=22500 meters 2.

Example online geometry solving problem 2:

A perimeter of the triangle is 50cm. If 2 of its sides are equal and also the third side is 5cm more than the equal sides, find the length of the third side?

Solution:

Let x = length of the equal side.

Third side=5 more than the equal side=x+5

So, the three sides are x, x and x+5.

P = sum of the three sides

x+ x+(x+5) =50

Combine like terms

3 x + 5=50

3x = 50 – 5

3x = 45

x =15cm (equal sides)

Length of the third side=x+5=15+5=20cm

The length of third side is 20cm.

Example online geometry solving problem 3:

A circle has an area of 100pi square units. What is the length of the circle's diameter and circumference?

Solution:

Area of the circle

A = (pi)*r^2

100pi = (pi)*r^2

(100pi) / pi = [(pi)*r^2] / pi

100= r^2

10 = r

So, the radius=10units

Diameter=2(radius) =20 units

Circumference= (pi)*d

=20pi units (or)

Substitute the value of pi=3.14

=62.8units

Circumference=20pi units (or) 62.8 units.

Understanding Quadratic Equation Calculator is always challenging for me but thanks to all math help websites to help me out.

Practice problems for online geometry solving:


Problems:

A circle has an area of 80pi square units. What is the length of the circle's diameter and circumference?
Answer: 16 pi units.

A circle has an area of 60pi square units. What is the length of the circle's diameter and circumference?
Answer: 12 pi units.

Solving 5th Grade Geometry Problems

Introduction to 5th Grade geometry problems:

Geometric is construction of object form given measurement.5th grade geometry contains the topic of  Understanding what is meant by point, line, and plane Identifying acute, right, obtuse, and straight angles as well as complementary angles, supplementary angles, and vertical angles Identifying parallel lines and perpendicular lines. 5th grade geometric contains the content of triangle, square, circle, rectangle, used to finding the area and volume of the given figure.


Solving Example problems in 5th grade geometry:


5th grade geometry Problems in angle:

Example 1:

1. Which of the following can be the angles of a triangle?

(a)90°, 45°, 55° (b)30°, 70°, 80°(c) 45°, 80°, 50°

Solution:

(a)Sum of the three angles = 90° + 45° + 55° = 190° > 180°

Hence, these cannot be the angles of a triangle.

(b)Sum of the three angles = 30° + 70° + 80° = 180°

Hence, these can be the angles of a triangle.

(c)Sum of the three angles = 45° + 80° + 50° = 175° < 180°

Hence, these cannot be the angles of a triangle.

5th grade geometry Example Problems :

Example 2:

2. find the area of the triangle, its base =4cm and height =6cm?

Solution:

Area of triangle=1/2(Base * height)

=1/2(4*6)

=2*6

=12cm

Problems in square:

A square is a closed figure made up of four line segments

Its side lengths are equal.

Area of square =(side * side)

Perimeter of square =4*side

Having problem with Volume of a Pyramid keep reading my upcoming posts, i will try to help you.

5th grade geometry Example Problems :


Example 3:

3.Find the area and perimeter of  square which side length is 5?

Solution

Side of the square=5m

The perimeter of the floor is given by P= 4×side

=4×5m = 20m

Thus, the perimeter is 20 m.

Area =side * side

=5*5

=25cm2

Problems in circle:

Example 4:

Length of the diameter = 2 × length of the radius

Find the diameter of the circles whose radii are:

(a)2 cm(b)5 cm (c)4.5 cm

Solution:

We have Diameter = 2 × radius

= 2×2cm

= 4cm

Diameter = 2 × radius

= 2×5cm

=10cm

Diameter = 2 × radius

= 2 × 4.5 cm

= 9 cm

Problems in rectangle:

Example 5:

Area of rectangle: Length * Width)

Perimeter of rectangle=2(length+ width

Find the area of rectangle which length is 4 and breath is 7?

Area of rectangle: Length * breath

=4*7

=28cm2

Introduction to Co-ordinate Geometry

Introduction to co-ordinate geometry:
Co-ordinate geometry is a branch of Mathematics that studies about points, lines and geometrical figures using co-ordinate systems. In geometry, we study the same using geometrical constructions and actual measurement but in co-ordinate geometry it is predominantly using co-ordinates of points.

Some of the topics covered in co-ordinate geometry are  finding distance between two points, slope of line, equations of lines, circles and geometrical figures etc

Let us solve some of co-ordinate geometry problems to get a feel of the subject

Understanding Vertex Form of Parabola is always challenging for me but thanks to all math help websites to help me out.

Solve Points Problems of Co-ordinate geometry:


Problem 1:

Find the slope of the line for these two points. ( 5 , 6 ) and ( -3 , 9 )

Solution:

The slope formula is given by

m = `(y2-y1)/(x2-x1)`

Given two points: (x1, y1) =  (5, 6) and (x2, y2) = (-3, 9)

Apply these two points into that formula for finding slope.

m = `(9-6)/(-3-5)`

m = `3/-8`

m = `- 3/8`

The slope of these two points is `-3/8` .

Problem 2:

Solve the distance for the given two points (5, 4) and (4,6)

Solution:

The distance formula is given by

d = `sqrt((x2-x1)^2+(y2-y1)^2)`

d = `sqrt((4-5)^2+(6-4)^2)`

d = `sqrt((-1)^2+(2)^2)`

d = `sqrt(1+ 4)`

d = `sqrt(5)`

The distance for these points is 2.23.


Solve Lines problem of Co-ordinate geometry:


Problem:

Solve the equation of a line between these two points (3, 8) and (-6, 4).

Solution:

Line equation form is y = mx + b

Solve m, slope between these two points.

The slope formula is given by

m = `(y2-y1)/(x2-x1)`

Given two points: (x1, y1) =  (3, 8) and (x2, y2) = (-6, 4)

Apply these two points into that formula for finding slope.

m = `(4-8)/(-6-8)`

m = `-4/-14`

m = `4/14` ---------------Simplify it.

m = `2/7`

Solve b, y intercept

For one point (x1, y1) = (3,8), the line equation becomes

y1 = mx1 + b

8  = `2/7` (3) + b

8  =  `6/7`   + b

b = 8 – `6/7`

b = `50/7`

Substitute m and b into line equation, we get

y = mx + b

y = `2/7` x + `50/7`

y = `1/7` (2x+50)

Multiply by 7 both on sides,

7y = 2x + 50

2x – 7y +50 = 0.

So the equation of line between these two points is 2x – 7y + 50 = 0.


Solve Circle Problem of Co-ordinate geometry:


Problem:

Find the center and radius of (x – 5)^2 + (y – 7)^2 = 25 circle.

Solution:

The circle equation form is (x-h)^2 + (y-k)^2 = R2.

Here the center is (h, k) and Radius is R.

The given equation looks the same as circle equation form.

(x-5)^2 + (y-7)^2 = 52

From the given equation, the center is (5, 7) and Radius is 5.

Solve Geometry Placement Test

Introduction to solve geometry placement test:

The division of math which deals with the measurement of lengths, angles, areas, perimeters and volumes of plane and solid figures is called geometry.we all knew placement is our dream in college life.In placement test, geometry plays an important role.Here solved geometry placement test papers with solutions given for your practice. Sample geometry placement test paper were given solve this test on your own without the help of a calculator, book, notes, or other people.


Solve geometry placement test:


Example 1:

A room inner space of diameter 150 cm has a wall around it. If the length of the outer edge of the wall is 60 cm, then find the width of the wall.

Solution:

Diameter of the room = 150 cm

Radius = 150 / 2 = 75 cm

Let width of wall = x cm then total radius = (75 + x) cm

Outer edge of the wall = 2  pi  (75 + x) = 44/7  (75 + x) cm

But outer edge of wall = 660 cm

44/7 (75 x) = 660

75 + x = 660  7 / 44

= 105

X = 105 - 75

X = 30 cm

Example 2:

Find number of times will the wheel of a car rotate in a journey of 76 km if the diameter of the wheel is 36 cm?

Solution:

Diameter of the wheel = 36 cm

The Circumference of the wheel of diameter  =  D = 22 / 7  36 = 113 cm

Length of the journey = 76 km = 76*1000*100 cm

Number of times the wheel will rotate in covering the above journey

= `7600000 / 113`

= 67,256.63 .

Please express your views of this topic Volume of Triangular Prism by commenting on blog

Solve geometry placement test:Examples


Example 3.

Find the area of a rectangle of length = 9 cm,breadth = 6 cm.

Solution:

Length and breadth is given here,

we need to find the area ,

Area = l × b sq.units

=` 9 * 6` sq.cm

= 54 sq.cm

Example 4.

Find the perimeter of a rectangle of length = 6 cm,breadth = 5 cm.

Perimeter = 2 (l + b) units

Perimeter  =  2 (6 + 5) units

= 22 cm.

Example 5:

A piece of thin wire which is circular, converted into a square of side 7cm. find the radius of circular wire.

Solution:

Side of a square = 7 cm

Its perimeter = `4* side` = `4 * 7` cm = 28 cm

Circumference of the circular wire = 28 cm. we know that c =`2*pi*r`

28 =` 2*(22/7)*r`

r = `(28*7)` /` (2* 22)`

= `196 / 44`

r = 4.454 cm

Transformations Geometry

Introduction for transformations geometry:

The transformation Geometry is a copy of a geometric figure, where the copy holds some certain property. The original shape is called the pre-image the new picture is called the image of the transformation. A transformation is single in which the pre-image and the figure equally has the exact same dimension and shape. I like to share this Definition of Parabola with you all through my article.


Basic Transformation Geometry:


The two types of transformation geometry is given by

Rigid transformations

Non-rigid transformations.

This page will covenant with three rigid transformations known as translations, reflections and rotations.

About geometry transformations:

The main geometry transformations in the mathematics are given as,

Translations

Reflections

Rotations

Scaling

Shear

Translations:

The mainly basic transformation is the translation. The definition of a translation is the pre-image and then it can be moved to the equal distance in the same direction to form the image .The transformation is would be

T(x, y) = (x+7, y+4).

Reflections:

The reflection is a "flip" of an aim over a line.

The two very common reflections is given by

horizontal reflection

vertical reflection.

The line of reflection will be both red points, blue points, and green points. The line of reflection which is directly in the center of both points. Having problem with Surface Area of a Circle keep reading my upcoming posts, i will try to help you.


Other types of Transformations:


Rotations:

The transformations which are performed by spinning the object just about a point of the center rotation .You can able to change your object at some of the degree measure, but 90° and 180° are very important degrees.

Rotation 180° around the origin: T(x, y) = (-x, -y)

Scaling:

The scaling is a linear transformation which diminishes the objects and the scale factor is same for direction is called scaling. The resultant image of the uniform scaling is similar to the original transformations

Shear:

The Shear which transforms effectively to rotate one axis and that the axes are no longer at right angle. A rectangle becomes a parallelogram, and a round becomes an ellipse. Constant lines parallel to the axes continue the same length, others do not. As a plot of the plane, it deception in the class of equilateral mappings.

Geometry Definitions

That branch of mathematics which investigates the relationship, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.


Line


In geometry a line:

·         is straight (no curves),

·          has no thickness, and

·         extends in both directions without end (infinitely)


Line segment:


If it does have ends it would be called a "Line Segment".

"Line" normally means straight, so say "curve" if it has a curve.

The word "segment" is significant, because a line normally extends in both directions without end.


angle-angle-angle (AAA) similarity


The amount of turn between two straight lines that have a common end point (the vertex). An acute triangle is a triangle with all angles lesser than 90 degrees.

The angle-angle-angle (AAA) relationship test says that if two triangles have corresponding angles that are congruent, then the triangles are similar. Because the sum of the angles in a triangle must be 180°, we really only need to know that two pairs of corresponding angles are congruent to know the triangles are similar.

The centroid of a triangle is the point where the three medians meet. This point is the center of mass for the triangle. If you cut a triangle out of a piece of paper and put your pencil point at the centroid, you could balance the triangle.Having problem with Surface Area Sphere keep reading my upcoming posts, i will try to help you.


Congruent


Two figures are congruent if all corresponding lengths are the equal, and if all corresponding angles have the same measure. Colloquially, we say they "are the same size and shape," though they may have different orientation. (One might be rotated or flipped compared to the other.)

Sat Geometry Problems

Introduction of sat geometry:
The Abbreviation of SAT is Scholastic Aptitude Test. This test is used for admission to college in United States. The total time has given for SAT test is 70 minutes.There are two sections , one section is given 50 minutes, another section is given 20 minutes.

Topics of sat geometry:

Area and perimeter of a polygon in sat geometry

Area and circumference of a circle in sat geometry

Volume of a box, cube and cylinder in sat geometry

Pythagorean Theorem in sat geometry

Coordinate geometry in sat geometry

Slope

Triangles


SAT Geometry Problems


Problem1:

Which one of these have the largest volume?

Square based prism with sides 7

Rectangular prism of dimensions 5x5x4

Rectangular prism of dimensions 5x6x8

Cylinder of base radius 3 and height 6

Cylinder of base radius 3 and height 8

Problem 2:

My triangular prism has a triangle base with base 5 and height 6, and the prism has a height of 7. What is the volume of the triangular prism?

96

24

100

84

105

Problem 3:

My shape has 4 sides. One of which are parallel. The sides are not all equatl. What shape do I have?

Parallelogram

Trapezoids

Rhombus

Prism

Problem 4:

I have a polygon with 6 equal sides that has 6 equal angles. What is the size of each angle?

180

120

90

154.3

720

Problem 5:

What is the equation of a line with slope is -2 and y intercept is -1 is ?

2x-y+2=0

2x+y+1=0

2x+y-1=0

Is this topic Area of Ellipse hard for you? Watch out for my coming posts.

Problem 6:


The slope of the line 3x+4y+5 = 0 is

3/4

4/3

-3/4

Problem 7:

The straight line x+2y+7=0 passes through (3,k) then valuee of k=?

5

-5

0

Problem 8:

Equation of line parallel to y-axis and passing through the point (3,2) is ?

X = 3

x = -3

y = -3

Problem 9:

A line passing through (0,3) and (4,5) is ?

x – 2y +6 = 0

2x – y + 6 = 0

x – 2y - 6 = 0

Problem 10:

What is the perimeter of my triangle with given three vertices (2,3), (6,2) and (4,2)?

9.7

9.0

8.9

7.9

Solve Geometry Exam

Introduction to solve geometry exam:

Geometry is a branch of mathematics that can be deals with the size, shape, position of shapes, and the properties of space. The geometry is also deals with the applications such as surveying, measurements, areas, and volumes. In Theoretical geometry or pure geometry, we give proofs for theorems on the properties of geometrical figures by applying axioms and reasoning. In practical geometry, we do not construct exactly the geometrical figures but draw rough sketches of the figures to give support to our logical reasoning. I like to share this Quadrilateral Formula with you all through my article.


Example problems to solve geometry exam:


Example problems to solve geometry exam are as follows:

1) The side length of cube is 10 cm. Find the volume of the cube.

Solution:

Formula for volume of the cube = a^3.
a= side length of the cube.

a=10 cm.

= (10)^3.

Volume of the cube =1000 cm^3.
This is the solution for the given geometry problem.


2)A triangle has a perimeter of 56. If 2 of its sides are equal and the third side is 8 more than the equal sides, what is the length of the third side?

Solution:

Let y = length of the equal side


Perimeter = sum of three sides.
Plug in the values from the question.
56 = y + y + y + 8

Combine like terms
56 = 3y + 8

3y = 56 – 8 (by equating the given equation)
3y = 48
y =16

Note: the third side is 5 more than the equal sides.

So, the length of third side = 16 + 8 =24

Answer: The length of third side is 24



Additional problems to solve geometry exam:


Additional problems to solve geometry exam are as follows:

1)The ratio of two supplementary angles is 12 to 6. Find the measure of each angle.

Solution:

Let measure of smaller angle = 12x, measure of larger angle = 6x.
12x + 6x = 180° (The sum of supplementary angles is 180°.)

18x = 180°

x = 10°
Then, 12x = 12(10°) and 6x = 6(10°).

So, 12x = 120° and 6x = 60° (by equating the given equation)

The angles have measures of 120° and 60°.
This is the solution for the given geometry example problem.

Geometry Terms and Definitions

Introduction to learning geometry terms and definitions:
Geometry is a branch of mathematics which  deals with the study of different shapes. Also learning the geometry terms and definitions include certain constructions of geometry such as lines, angles, plane etc., the word geometry is derived from the two words ‘geo’ meaning ‘earth’ and ‘metron’ meaning measuring. The geometry of plane figures are known as Euclidian geometry or plane geometry. I like to share this Skew Lines Examples with you all through my article.


Learning Terms and definitions of geometry:


There are various terms and definitions involved in geometry. Some of the terms and definitions involved in geometry for learning are listed below:

1. Point:

In geometry a point is a location in space with a dot on a piece of paper is known as point.

2. Mid point:

A segment that can be divides into two with equal length are known as mid point.

3. Square:

It has all the sides are equal with angles are equal to 90°. Then their diagonals are equal and they bisect at right angles.

4. Line:

The region where two points connects via the shortest path and continues indefintely in both the directions is referred as a line.

5. Line segments:

In geometry a line segments is a part of a line between the two points.

6. Perpendicular line segments:

If a line segments that intersect or cross at an angle of 90°. Then is it known as perpendicular line segments.

7. Parallel line segments:

If a line segments that never intersect or they can always in the same distance apart is known as parallel line segments.

8. Parallelogram:

The opposite sides are equal and parallel and opposite angles are equal. The diagonals are bisect to each other. Understanding Volume of Rectangular Prism is always challenging for me but thanks to all math help websites to help me out.


Learning terms and definitions of geometry for triangles and circles:


Learning terms and definitions of geometry for triangles and circles includes the following:

1. Right angle:

Angle that measures 90° is referred as right angle

2. Rectangle:

Their opposite sides are equal and parallel with the angles are equal to 90°..

3. Acute angle:

Angle that measures less than 90° is referred as acute angle

4. Obtuse angle:

An angle that measures more than 90° is referred as Obtuse angle.

5. Isosceles triangle:

A triangle with two equal length sides and also with two equal internal angles is referred as an isosceles triangle.

6. Equilateral triangle:

If a triangle has the equal length on all three sides, then it is referred as equilateral triangle.

7. Circles:

A circle has a locus of all points which equidistant from the center of a point.

8. Circumference:

The distance around a circle is called the circumference of a circle.

9. Concentric circles:

If the circles having the same centre but different radii are called concentric circles.

10. Tangent of circle:

If a line perpendicular to the radius, then, it can touches only one point on the circle.

Geometry Tests

Introduction:

Geometry is a part of mathematics. It used to calculate the measurements of angles, lines, surfaces and solid shapes. Geometry is using for depicting all kinds of shapes and their properties. Please express your views of this topic Tangent Line Problem by commenting on blog.

There are two main classifications in Geometry.

1) Plane Geometry

2) Solid Geometry


Example problems:


Problem 1: Find the volume of cone with radius 6 cm and height 10 cm.

Solution:

Given: Radius = 6 cm

Height = 10 cm.

Volume of cone = `(1/3)` * ` pi` * radius2 * height

= `(1/3)` * 3.14 * 62 * 10

= 0.33 * 3.14 * 36 *10

= 373.032 cubic cm.

The volume of cone is 373.032 cubic cm

Problem 2: Find the Perimeter of Parallelogram for the side a is 5 and side b is 9.

Solution:

Given: Side a = 5

Side b = 6

Perimeter of Parallelogram P = (2 * 5) + (2 * 9)

P = 10 + 18

P = 28

The Perimeter of Parallelogram is 28


Problem 3: Find the circle area and circumference radius with 6 cm.

Solution:

Given: Radius = 9 cm

Area of Circle = `pi ` * radius2

= 3.14 * 62

= 3.14 * 36

= 113.04 square cm.

The Area of Circle is 113.04 square cm

Circumference of Circle = 2 * `pi` * radius

= 2 * 3.14 * 9

= 37.68 cm

The circumference of circle 37.68 cm

Problem 4: Find the Area of triangle with height 3 cm and Base 4 cm.

Solution:

Given: Height = 3 cm

Base = 4 cm

Area of Triangle = (1/2) * height * base

= 0.5 * 3* 4

= 6 square cm

The Area of Triangle 6 square cm

Problem 5: Find the Area of Triangle with height 10 cm and Base 12 cm.

Solution:

Given: Height = 10 cm

Base = 12 cm

Area of Triangle =(1/2) * height * base

= 0.5 * 10* 12

= 60 square cm

The Area of Triangle =  60 square cm

Problem 6: Find the Perimeter of Parallelogram of  the side a is 7 and side b is 8.

Solution:

Given: Side a = 7

Side b = 8

Perimeter of Parallelogram P = (2 * 7) + (2 * 8)

P = 14 + 16

P = 30

The Perimeter of Parallelogram = 30

Problem 7: Find the circle area and circumference radius with 7 cm.

Solution:

Given: Radius = 9 cm

Area of Circle = π * radius2

= 3.14 * 72

= 3.14 * 49

= 153.86 square cm

The area of circle 153.86 square cm

Circumference of Circle = 2 * π * radius

= 2 * 3.14 * 7

= 43.96 cm

The Circumference of Circle = 43.96 cm

Solving Geometric Angles

Introduction for solving geometric angles:

The figure which consists of two rays with the same starting point and the angle which can be formed by the two arms on either side of the initial point and it is the vertex angle .There are different types of angles which based on their measuring degrees. Now we are going to see about the solving of geometric angles.


Types of solving geometric angles:


The different types of solving geometric angles is given by,

Right angle

Acute angle

Obtuse angle

Straight angle

Complementary angle

Supplementary angle

Right angle:

A right angle whose measure is 90°, is called a right angle.
Acute angle:

An acute angle whose measure is less than 90° is called an acute angle.

30°, 60°, 70° etc are all acute angles.

Obtuse angle:

An Obtuse angle whose measure is greater than 90° is called an Obtuse angle

120°, 135°, 140° etc are all Obtuse angle

Straight angle:

A Straight angle whose measure is 180° is called a Straight angle

Complementary angle:

A complementary angle is nothing but the sum of two angles measures 90° are called complementary angles.

30°, 60° are complementary angles .

Supplementary angle:

A supplementary angle is nothing but the sum of the two angles which measures 180° are called Supplementary angles.

120°, 60° are Supplementary angles. I have recently faced lot of problem while learning geometry tutoring online free, But thank to online resources of math which helped me to learn myself easily on net.


Example for solving geometric angles:


Ex1:

A geometric angle is 14° more than its complement. What is its measure?

Sol:

Let x° be the required angle.

Its complement=90°-x°

By the given condition:

90°-x°+14°=x°

2x°=104°

X°=52°

Hence required angle=52°

Ex2:

The measure of an geometric solving angle is double the calculate of its supplementary angle. Find its measure.

Sol:

Let the required angle =x°.

Its supplementary angle =180°-x°

By the given condition =2(180°-x°)

=360°-2x°

=120°

Hence required angle=120°

Ex3:

The two supplementary angles are the ratio2:3.Find the angles .

Sol:

Let the two angles in degrees be 2x and 3x

By the given condition=2x+3x=180°

5x=180°

X=36°

Hence the required angles are 2×36°=72° and

3×36°=108°

Geometry Practice Problems

Introduction for learning geometry problem answers:

The subdivision  of mathematics concerned with the properties of lines, curves and surfaces usually divided into pure, algebraic and differential geometry in accordance with mathematical techniques utilized.  The figures of two dimensions is called planes. learning Geometry problem answers is a module of math which involves about the study of shapes, lines, angles, dimensions, relative position of figures etc. it plays vital role in real time application like elevation, projection. Learning geometry problems answers provides many foundational skills and helps to build the thinking skills of logic, deductive reasoning, and analytical reasoning.Let us learn geometry problem answers. I like to share this What are Similar Triangles with you all through my article.


learning geometry problem answers:


A triangle has a perimeter of 56. If 2 of its sides are equal,then the  third side is 5 more than the equal sides, what is the length of the third side?

Solution:

Let y = length of the equal side
perimeter of triangle.

Perimeter of a  triangle = sum of all the 3 sides.
Plug in values of question.
56 = y + y + y + 5

Combine like terms
56 = 3y + 5

3y = 56 – 5
3y = 51
y =17

Note: the third side is 5 more than the equal sides.

So, the length of third side = 17 + 5 =22

Answer: The length of third side is 22.

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learning geometry problem answers:


The perimeter of a rectangle is 400 meters and its length is 3 times its width W. Find Width and Length, and the area of the rectangle.

Solution:

Use the perimeter formula to write.

2 L + 2 W = 400
"its length is 3 times its width W" into a mathematical equation as follows:

L = 3 W
We substitute L = 3 W in the equation 2 L + 2 W = 400.

2(3 W) + 2 W = 320
Expand and group like terms.

8 W = 400
Solve for W.

W = 50 meters
Use the equation L = 3 W to find L.

L = 3 W = 150 meters
Use the formula of the area.

Area = L x W = 150 * 50 = 7500 meters 2.

Geometry Questions

Introduction :

Geometry is a section in math, which deals with many aspects regarding shapes, figures. they involve with construction, study of their properties, area , volume, etc. They include study of solids too. Geometry deals with the entire concepts related to the shapes, solids, etc. Sample questions about the intersecting lines, area are in the following section.


Example geometry questions:


Here are few example geometry questions:

Geometry question 1:

Find the area of the triangle formed by (5,2), (-9,-3), (-3,-5)

Solution:

The formula for finding the area of the triangle formed by  (x1,y1), (x2,y2), (x3,y3)  is 1/2 | [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] |

Applying the formula,we get

1/2 | [5(-3 + 5) -9(-5 -2) -3(2 + 3)]|

1/2 |10 + 63 – 15|

1/2 |58|

Hence the area of the triangle is 29.


Geometry question 2:

Find the point which divides the line segment joining (-1,2) and (4,-5) in the ratio 3:2

The formula for a point which divides the line joining A(x1,y1) and (x2,y2) in the ratio l:m is

`((lx2 + my1)/( l + m) ,(lx2 + my1)/( l + m)) `

Applying the formula,

The point is

`((3 * 4 + 2 * (-1)) /( 3 + 2) , (3 * (-5) + 2 * 2)/(3 + 2))`

`((10)/(5),(-11)/(5))`

Hence the point is (2,-11/5)

Geometry Shapes Definitions

Introduction to Definitions of Geometry Shapes :

A branch of mathematics concerned with the properties of lines, curves and surfaces usually divided into pure algebraic and differential geometry in accordance with the mathematical techniques utilized. Here we have to learn about different geometry shapes definition. Please express your views of this topic Types of Quadrilaterals by commenting on blog.

List of Different geometry shapes whose definition follows:

Triangle

Quadrilateral

Pentagon

hexagon

Heptagon

Octagon

Square

Circle


Definitions of Geometry shapes - Triangle, Quadrilateral, Pentagon ,Heptagon, Octagon:


Triangle:A triangle is defined as a polygon with three vertices and three sides which are line segments. A triangle with vertices X, Y, and Z is denoted triangle XYZ.It is generally classified as there types they are isosceles, equilateral, and scalene triangle.

Quadrilateral:It is a plane figure having four straight sides. The word quadrilateral is made of the words quad represents the four similarly laterals represents the sides. The sum of interior angles equal to 360 degree. There are many types of quadrilateral are there like trapezoid, parallelogram, rectangle, kite.

Pentagon:A 5-sided polygon (a flat shape with straight sides)

Heptagon:A plane figure having seven sides. If all the interior angles of a heptagon are equal then it is known as regular heptagon .It is also called as septagon.

Octagon:An 8-sided polygon (a flat shape with straight sides).

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Definitions of Geometry shapes - Square, Circle, Hexagon:


Square:A 4-sided polygon (a flat shape with straight sides) where all sides have equal length and every angle is a right angle (90°)

Circle:It is a plane curve formed by the set of all points of a given fixed distance from a fixed point .The fixed point is called the centre and the fixed distance the radius of the circle.

Hexagon:A polygon with six sides. A regular hexagon has all its side of equal length and hence all vertical angles are equal and each being 120 degree. A vertex contains 3 diagonals and hence it has fully 9 diagonals.

Geometry Exam Questions

Introduction to Geometry exam questions:

Geometry is a part of mathematics which is related with the questions of size, relative position of figures and with properties of space. Geometry is one of the branches of sciences. A physical arrangement will  show geometric forms or lines.

Geometry analyzes the relations, properties, and the measurement of solids, planes, lines, and angles the science which covers of the properties and relations of magnitude the geometry of the relations of space.

Preparation for the geometry exam questions are essential. Some of the geometry exam questions are given below: Having problem with Exterior Angles Definition keep reading my upcoming posts, i will try to help you.


Geometry Exam Questions:


Find the correct answer to the following geometry exam questions

Q 1: If the circle has diameter of 8, what is the circumference?

A. 6.28

B. 12.56

C. 25.13

D. 50.24

E. 100.48

Answer: A

Q 2: Identify the form of the statement All City College students love math.

a)If a person loves math, then the person is a City College student.

b)If a person is a City College student, then the person loves math.

c)If the person is not a City College student, then the person does not love math.

d)None of the above

Answer: B

Q 3: Name the property of equality that can justifies the statement, If m1+25=180 , then m1=155 .

a) Symmetric

b) Transitive

c) Substitution

d) Subtraction

Answer: D

Q 4: Find the measures of the sides of the equilateral delta PQR if PQ=5x-7 and PR=2x+5.

a)39

b)4

c)12

d)13

Answer: D

Q 5:  All the parallelogram have

a) opposite angles that are supplementary.

b) diagonals that are congruent.

c) four congruent opposite sides that are congruent.

Answer: D


Additional geometry exam questions:


Q 1:  Name the property of the equality that justifies the statement, If m1+25=180 , then m1=155..

a) Symmetric

b) Transitive

c) Substitution

d) Subtraction

Answer:D

Q 2:  What symbol is used to indicate in writing the two line segments are identical?

a)  //       b)=   c) ?       d)?

Answer: D

Q 3: What is the principle basis of the inductive reasoning?

a) Postulate   b) Past Observation     c) Definitions      d) Theorems

Answer: B

Q 4:

Two circles both of radii 6 have exactly one point in common. If A is a point on one circle and B is a point on the other circle, what  is the maximum possible length for the line segment AB?

a) 12   b) 15     c)24    d)20

Answer: C

Geometry Congruence

Definition for geometry congruence:

In Geometry, we study different figure, their properties the relations between them. Every figure has its shape, size and Position. Given two figures you can easily decide whether they are of the same shape.

Figures having same shape and size  and angles are called congruent. Congruent means equal in all respects of the given figure. If two figures are congruent then it means that the size, shape and measurement of the first figure correspond to the size, shape and measurements of the second figure. I like to share this Symbol for Congruence with you all through my article.


Congruence for geometry:


If two persons compare the size shape of their fore-hands, they will do so by comparing thumb with thumb, fore-finger with fore-finger etc. Thus thumb corresponds to thumb. Similarly the two fore-fingers correspond to each other.

When we put a figure on another figure in such a way that the first figure covers the other figure completely i.e. all parts of the first figure completely cover the corresponding parts of the other. Then these figures will be said to be congruent to each other.

The relation property of two figures being congruent is called congruence. When two figures are congruent we denote them symbolically as. One figure ≅ second figure. The property of congruence, as you know is symbolically represented as ≅.


Important points in congruence of geometry:


Congruency in geometry means to be equal in all respect.
Two figures can be said to be congruent only when all parts of one are equal to the corresponding parts of the other.
The property of congruence of figures is called congruency.
If two line segments are congruent then they must have the same length.
If two angles are congruent then their measures must be equal.
Two triangles are congruent only
Two squares are congruent if they have the same side length.
Two rectangles are congruent if they have the same length and breadth.
Two circles are congruent if they have the same radius.
Sum of the three angles of a triangle is equal to 1800 therefore. if the measures of any two of them are given the third can be ascertained.

Coordinate Systems Geometry

Introduction of coordinate systems geometry:

Geometry is one of the basic and oldest topics in the mathematics. Geometry is used to study the characteristics and properties of the figure. Let every point on a straight line is associated with exactly one real number only. Rene Descartes, a mathematician who is the first man to introduce an algebraic geometry of coordinate systems. A plane is a collection of points in a space of the coordinate systems of geometry.Is this topic Lateral Area of a Rectangular Prism hard for you? Watch out for my coming posts.

About the coordinate systems:


Let us consider a sheet of the paper as the plane and draw two fixed perpendicular straight lines in that plane of the paper which will be intersecting at a point.

We always draw a straight line in horizontal direction and the other line will be a vertical line. These two lines which will meet at a common point and it is named as O and called the origin.

We represents that the horizontal as x–axis and the vertical line as y–axis.

The two lines which divides the plane into four parts namely quadrants. These quadrants are named as I quadrant, II quadrant, III quadrant and IV quadrant in geometry systems.

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Constructing co-ordinates system geometry:


Consider any point P in the plane. This point P lies in a quadrant.

From P, draw a straight line parallel to the y–axis to meet the x–axis at the point L, and draw a straight line parallel to the x–axis to meet the y–axis at the point M.

Let 'a' representing the point L on x–axis and 'b' representing the point M on y–axis.

If P lies on the x– axis, then b = 0.If a = 0, then a> 0 and b > 0. If a < 0 and b > 0, then P lies within the II quadrant.

If P lies within the III quadrant, then a< 0 and b < 0. If a > 0 and b < 0, then P lies within the IV quadrant If P is the point O, then a = 0 and b = 0. The number a is called the x–coordinate of the coordinate system of point P and the number b the y–coordinate of the coordinate systems of geometry.

The plane now is called the rectangular coordinate plane systems or the xy–plane.