NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2

Class VIII Mathematics NCERT book Ex. 3.2 of chapter 3 Understanding Quadrilaterals in PDF file format free to download or use online without downloading. All the solutions of questions in exercise 3.2 of class 8 mathematics are done properly step by step. We have provided the CBSE solutions in simple way with best way of solution and easy to understand. If anyone face problem during the use of NCERT Solution App or website call us for without any hesitation.

A closed figure bounded by three or more line segments is called a polygon. A polygon is said to be regular, if it is both ‘equiangular’ and ‘equilateral’. A polygon is named according to the number of sides it contains.

Similarly, nine-sided figure is called nonagon and ten-sided figure is called decagon.

• (i) The four points A, B, C, D are called its vertices,
• (ii) The four line segments AB, BC, CD, and DA are called its sides,
• (iii) ∠DAB, ∠ABC, ∠BCD and ∠CDA are called its angles to be denoted by ∠A, ∠B, ∠C and ∠D respectively, and
• (iv) The line segments AC and BD are called its diagonals.

Two sides of a quadrilateral which have a common end point are called its adjacent sides. In the given figure, (AB, BC), (BC, CD), (CD, DA) and (DA, AB) are four pairs of adjacent sides of quad. ABCD.

Two sides of a quadrilateral are called its opposite sides if they do not have a common end point.
In the given figure, (AB, DC) and (AD, BC) are two pairs of opposite sides of quad. ABCD.

Two angles of a quadrilateral having a common arm are called its adjacent angles. Opposite Angles of a Quadrilateral Two angles of a quadrilateral which are not adjacent angles are known as opposite angles. In the given figure, (∠A, ∠C) and (∠B, ∠D) are two pairs of opposite angles of quad. ABCD.
In the given figure, (∠A, ∠B), (∠B, ∠C), (∠C, ∠D) and (∠D, ∠A) are four pairs of adjacent angles of quad. ABCD.

Proof:
Let ABCD be a quadrilateral, Join AC.
Clearly, ∠1 + ∠2 = ∠A … (i)
And, ∠3 + ∠4 = ∠C … (ii)
We know that the sum of the angles of a triangle is 180°.
So, from triangle ABC, we have ∠2 + ∠4 + ∠B = 180°.
From triangle ACD, we have ∠1 + ∠3 + ∠D = 180°.
Adding the angles on either side, we get:
∠2 + ∠4 + ∠B + ∠1 + ∠3 + ∠D = 360°.
Or, (∠1 + ∠2) + ∠B + (∠3 + ∠4) + ∠D = 360°.
Or, ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)].
Hence, the sum of the angles of a quadrilateral is 360°.

1. Opposite sides of a parallelogram are congruent.
2. Opposite angles of a parallelogram are congruent.
3. Consecutive angles in a parallelogram are supplementary.
4. The diagonals of a parallelogram bisect each other.

• 1) Opposite sides are congruent (they equal each other).
• 2) Opposite angles are congruent (they equal each other).
• 3) Consecutive angles are supplementary (they add up to 180).
• 4) Diagonals bisect each other (the parts are equal).
• 5) Diagonals are congruent (they equal each other).
• 6) All four corner angles are 90°.

• 1) Opposite sides are congruent (they equal each other).
• 2) Opposite angles are congruent (they equal each other).
• 3) Consecutive angles are supplementary (they add up to 180).
• 4) Diagonals bisect each other (the parts are equal).
• 5) Diagonals are congruent (they equal each other).
• 6) All four corner angles are 90°.
• 7) Diagonals perpendicular (the form right angles in the middle).
• 8) Diagonals bisect angles (the angles equal to each other).

1. Opposite sides are congruent (they equal each other).
2. Opposite angles are congruent (they equal each other).
3. Consecutive angles are supplementary (they add up to 180).
4. Diagonals bisect each other (the parts are equal).
5. Diagonals perpendicular (the form right angles in the middle).
6. Diagonals bisect angles (the angles are equal to each other).
7. All four sides are congruent.
8. The diagonals are NOT congruent.

1) Lower two base angles are congruent (they equal each other).
2) Upper two base angles are congruent (they equal each other).
3) The diagonals are congruent (they equal each other).
4) opposite angles are supplementary (they add up to 180).

• 1) Two pairs of consecutive sides congruent, but opposite sides not congruent
• 2) Diagonals perpendicular.
• 3) Exactly one pair of angles congruent.
• 4) One pair of angles bisected.