# NCERT Solutions for Class 8 Maths Chapter 4

NCERT Solutions for Class 8 Maths Chapter 4 PRACTICAL GEOMETRY in English Medium as well as Hindi Medium updated for new academic session 2021-22 based on latest CBSE Curriculum 2021-2022 and updated NCERT Books for current session.

Use online Prashnavali 4.1, Prashnavali 4.2, Prashnavali 4.3, Prashnavali 4.4 and Prashnavali 4.5 in Hindi Medium as well as English Medium updated for new academic session 2021-2022. Download Exercise 4.1, Exercise 4.2, Exercise 4.3, Exercise 4.4 and Exercise 4.5 in English Medium free to use online or download in PDF. NCERT Solutions 2021-22 for class 8 Maths are useful for all board whoever following the CBSE Curriculum 2021-2022. These solutions are based on updated NCERT Books 2021-22 for the academic session 2021-2022.

## NCERT Solutions for Class 8 Maths Chapter 4

 Class: 8 Mathematics Chapter 4: Practical Geometry

### Class 8 Maths Chapter 4 Solutions

Class 8 Maths Chapter 4 Practical Geometry all exercises in English Medium as well as Hindi Medium are given below to study online or download in PDF form for academic session 2021-22. Download Class 8 Maths App for offline use. It works without internet, once downloaded.

• ### 8 Maths Chapter 4 Solutions in Hindi Medium

#### Class 8 Maths Exercise 4.1 Solution in Videos

Class 8 Maths Exercise 4.1 Solutions
Class 8 Maths Exercise 4.1 Explanation

#### Class 8 Maths Exercise 4.2 Solution in Videos

Class 8 Maths Exercise 4.2 Solutions
Class 8 Maths Exercise 4.2 Explanation

#### Class 8 Maths Exercise 4.3 Solution in Videos

Class 8 Maths Exercise 4.3 Solutions
Class 8 Maths Exercise 4.3 Explanation

#### Class 8 Maths Exercise 4.4 Solution in Videos

Class 8 Maths Exercise 4.4 Solutions
Class 8 Maths Exercise 4.4 Explanation

#### Class 8 Maths Exercise 4.5 Solution in Videos

Class 8 Maths Exercise 4.5 Solutions
Class 8 Maths Exercise 4.5 Explanation

### More about Class 8 Maths Chapter 4

##### What are the main constructions in Class 8 Maths Chapter 4 NCERT Book?

There are main 5 types of constructions in Class 8 Maths chapter 4 as per NCERT Book. These are as follows:
When four sides and one diagonal are given.
When two diagonals and three sides are given.
When two adjacent sides and three angles are given.
When three sides and two included angles are given.
When other special properties are known.

##### Can we draw a quadrilateral uniquely if only the lengths of its four sides are given?

No, A quadrilateral can be constructed uniquely if the lengths of its four sides as well as a diagonal is given.

##### Can we draw a quadrilateral uniquely if its three sides and one included angle is given?

No, a quadrilateral can be constructed uniquely if its three sides as well as two included angles are given.

##### Can we draw a quadrilateral uniquely if its two diagonals and three sides are known?

Yes, it is possible.
A quadrilateral can be constructed uniquely if its two diagonals and three sides are known.

In Chapter 4 Practical Geometry, we have to learn how to construct a quadrilateral with the given specifications: like all four sides and two diagonals, sides, angles and one of its diagonals, three angles, a side and two diagonals etc. The following cases are important to do in this chapter:
1. A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are known.
2. A quadrilateral can be constructed uniquely if its three sides and two included angles are given.
3. A quadrilateral can be constructed uniquely if its two diagonals and three sides are known.
4. A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.

##### Things to know

Before any geometric composition, make a rough picture of it and by looking at it it becomes easy to determine which side or which angle to make first.

##### V. To Construct a Quadrilateral When 4 Sides and One Angle Are Given:

Construct a quadrilateral ABCD in which AB = 3.8 cm. BC = 3.4 cm, CD = 4.5, cm AD = 5 cm and ∠B = 80°. Steps of construction:
First we draw a rough sketch of quad. ABCD and write down its dimensions as given.
Step 1. Draw AB = 3.8 cm
Step 2. Make ∠ABX = 80°
Step 3. From B. set off BC = 3.4 cm.
Step 4. With A as centre and radius equal to 5 cm, draw an arc.
Step 5. With C as centre and radius equal to 4. 5 cm, draw another arc, cutting the previous arc at D. Step 6. Join AD and CD.
Then, ABCD is the required quadrilateral.

### Class 8 Maths Chapter 4 Important Questions

##### Draw a trapezium ABCD in which AB || DC, AB = 5 cm, AD = BC = 6.5 cm and ∠B = 60°.

Construct a quadrilateral ABCD in which AB || DC, AB = 5 cm, AD = BC = 6.5 cm and ∠B = 60°.
Steps of construction:
First we draw a rough sketch of quad. ABCD and write down its dimensions as given.
Step 1. Draw AB = 5 cm
Step 2. Make ∠ABX = 60°
(∠C = 1800 – 600 = 1200 because ∠C is supplementary angle of corresponding angle of ∠B)
Step 3. Make ∠BCZ = 120°
Step 4. With C as centre and radius equal to 6.5 cm, draw an arc cutting CZ at point D.
Then, ABCD is the required quadrilateral,

##### Construct a parallelogram ABCD in which AB = 6 cm, BC = 4.5 cm and diagonal AC = 6.8 cm.

Draw a rough sketch of the required parallelogram and write down the given dimensions.
Steps of construction:
(i) Draw AB = 6 cm.
(ii) With A as centre and radius 6.8 cm draw an arc.
(iii) With B as centre and radius 4.5 cm draw another arc, cutting the previous arc at C.
(iv) Join BC and AC.
(v) With A as centre and radius 4.5 cm, draw an arc.
(vi) With C as centre and radius 6 cm draw another arc, cutting the previously drawn arc at D.
(vii) Jon DA and DC.
Then, ABCD is the required parallelogram.

##### Construct a parallelogram, one of whose sides is 5.2 cm and whose diagonals are 6 cm and 6.4 cm.

We know that the diagonals of a parallelogram bisect each other.
Make a rough sketch of the required parallelogram, as shown.
Steps of construction:
(i) Draw AB = 5.2 cm.
(ii) With A as centre and radius 3.2 cm, draw an arc.
(iii) With B as centre and radius 3 cm draw another arc, cutting the previous arc at O.
(iv) Join OA and OB.
(v) Produce AO to C such that OC = AO and produce BO to D such that OD = OB.
(vi) Join AD, BC and CD.
Then, ABCD is the required parallelogram,

##### How do you know if 4 points form a quadrilateral?

A quadrilateral formed by the points A, B, C and D is complex, if the intersection of AB and CD (if any) lies between the points A and B, and the same applies for BC and DA.

##### How many set squares are needed to make a quadrilateral?

Thus a quadrilateral has 10 elements (4 sides, 4 angles and 2 diagonals) or measurements. To construct a unique quadrilateral, we need to know 5 measurements (elements). Note: To construct a unique quadrilateral simply the knowledge of any five elements is not sufficient.

##### How many sides does a regular polygon have if the measure of an exterior angle is 24 degrees?

Since the sum of the exterior angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equal exterior angles and therefore 15 vertices and sides to the polygon.                  