Question

prove that in a parallelogram opposite sides are equal

Answer 1

Consider a parallelogram ABCD.


AC and BD are the diagonals of the parallelogram.

Each diagonal of the parallelogram divides the parallelogram into two congruent triangles.

ΔADC ≅ ΔABC


∴ Corresponding sides of congrunt triangles are equal.
⇒CD = AB
⇒ AD = BC

Hence the opposite sides of the parallelogram are equal.

hope it helps u

Answer 2

Statement : In a parallelogram, opposite angles are equal.

Given : Parallelogram ABCD

To prove ; ∠A = ∠C and ∠B = ∠D

Proof :

In parallelogram ABCD,
Consider,

AD || BC and AB is transversal

∠A + ∠B = 180° [Co - int. Angles]...... (i)

Now, consider AB || DC and BC transversal

∠B + ∠C = 180° [Co - int. Angles]...... (ii)

From (i) and (ii) we get ;

∠A + ∠B = ∠B + ∠C
∠A = ∠C
∠B = ∠D

Hence, it is proved.