Question

proof that opposite angle of a parallelogram are equal

Answer 1

in the above figure it is proved

Answer 2

Given: A parallelogram ABCD

To prove: ∠A = ∠C and ∠B = ∠D

Proof: ABCD is a parallelogram.

Therefore, AD ll BC and AB ll DC

Now,

AD ll BC and transversal AB intersect them at A and B.

Sum of co - interior angles is 180°

$\therefore \: \angle A + \angle B = 180 \degree \: .........(i)$

Again,

AB ll CD and transversal AD interest them at A and D .

Sum of co - interior angles is 180°

$\therefore \: \angle A + \angle D = 180 \degree......(ii)$

$\sf{From \: (i) \: and \: (ii)}$

$\cancel {\angle A }+ \angle B = \cancel{\angle A } + \angle D$

$\angle B = \angle D$

$\sf{Similarly }\: \: \angle A = \angle C$

Hence, ∠A = ∠C and ∠B = ∠D