Class 8 Maths

# Practical Geometry

## Exercise 4.3

MO = 6 cm, OR = 4.5 cm, ∠M = 60°, ∠O = 105°, ∠R = 105°

• Draw MO = 6 cm
• Make an angle = 105° at point O.
• Draw OR = 4.5 cm
• Make an angle = 105° at point R
• Make and angle = 60° at point M
• Extend lines from points M and R so that they intersect at point E.

Here, sum of given three angles of given quadrilateral is = 60 + 105 + 105 = 270

So, fourth angle = 360 – 270 = 90

PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°

• Calculate fourth angle, i.e. ∠L = 360 – (90 + 110 + 85)
= 360 – 285 = 75
• Draw PL = 4 cm
• Make an angle of 90° on point P and another angle of 75° on point L.
• Draw LA = 6.5 cm
• Make an angle of 110° on point A
• Extend lines from P and A so that they intersect at point P

Question 3: Parallelogram HEAR

HE = 5 cm, EA = 6 cm, ∠R = 85°

• Draw HE = 5 cm
• Make an angle of 85° on point E
• Draw EA = 6 cm
• We know that adjacent angles are supplementary in a parallelogram.
• Supplement of 85° = 180° - 85° = 95°
• Make and angle of 95° on point A
• Draw AR = 5 cm so that it is parallel to HE
• Join H to R
• Parallelogram HEAR is complete.

Question 4: Rectangle OKAY

OK = 7 cm, KA = 5 cm

Answer: All angles of a rectangle are right angles and opposite sides are equal.

• Draw OK = 7 cm
• Draw KA = 5 cm perpendicular to OK
• Draw AY = 7 cm perpendicular to KA
• Join O to Y
• Rectangle OKAY is complete.

## Exercise 4.4

DE = 4 cm, EA = 5 cm, AR = 4.5 cm, ∠E = 60°, ∠A = 90°

• Draw DE = 4 cm
• Make and angle of 60° on point E
• Draw EA = 5 cm
• Make a right angle at point A
• Draw AR = 4.5 cm
• Join D to R

TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠R = 75°, ∠U = 120°

• Draw TR = 3.5 cm
• Make an angle of 75° on point R
• Draw RU = 3 cm
• Make an angle of 120° on point U
• Draw UE = 4 cm
• Join T to E

## Exercise 4.5

### Draw the following

Question 1: The square READ with RE = 5.1 cm

Answer: All sides of a square are equal and all angles are right angle.

• Draw RE = 5.1 cm
• Draw EA = 5.1 cm perpendicular to RE
• Draw DA = 5.1 cm perpendicular to EA
• Join R to D

Question 2: A rhombus whose diagonals are 5.2 cm and 6.4 cm long

Answer: We know that diagonals of a rhombus are perpendicular bisectors of each other

• Draw a vertical line = 6.4 cm
• Draw the perpendicular bisector of this line of length 5.2 cm
• Join four vertices to complete the rhombus

Question 3: A rectangle with adjacent sides of lengths 5 cm and 4 cm

Answer: All angles of a rectangle are right angles and opposite sides are equal.

• Draw a horizontal line = 5 cm
• Draw another line which is perpendicular to previous line and its length = 4 cm
• Draw a third line which is perpendicular to second line with length = 5 cm
• Draw a fourth line which is perpendicular to third line.
• Rectangle is complete.

Question 4: A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

• Draw OK = 5.5 cm
• Draw KA = 4.5 cm at any angle
• Draw YA||OK
• Draw OY||KA
• Parallelogram is complete.

This is not a unique parallelogram, because different parallelograms can be made by changing the value of the angle between first two lines.

## Rational Numbers

Any number which can be expressed in the form of p/q where q ≠ 0 is called rational number.

## Linear Equations

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

A plane figure bounded by a finite straight line segment in loop to form a closed chain is called a polygon.

## Data Handling

Learn about arranging data and making bar chart, histogram and pie chart.

## Probability

Probability of an outcome out of total events.

## Cube Roots

A number which is equal to another number raised to the power 3 is called a perfect cube.

## Algebraic Expressions

An expression with coefficient and variables is called algebraic expression.

## Mensuration

Learn to calculate area and perimeter of two-dimensional figures.

## Exponents Power

Exponents are used to represent a large number in simpler form.

## Proportion

A part compared to the whole is called proportion.

## Factorization

Factorization consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

## Graph

A graph is a pictorial representation of data to make it more user friendly.