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 .


Having problem with congruent triangles keep reading my upcoming posts, i will try to help you.

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.

Is this topic Completing the Square Formula hard for you? Watch out for my coming posts.

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.

Is this topic How to Find the Volume of a Hemisphere hard for you? Watch out for my coming posts.

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.