Question

Prove in a parallelogram that opposite angles are equal

Answer 1

Answer:

Step-by-step explanation:

Given: ABCD is a parallelogram

To prove: ∠A = ∠C and ∠B = ∠D

Proof:

AB||CD and AC is the transversal

Hence ∠1 = ∠4 → (1)

ΔABC ≅ ΔADC (SSS Congruence rule)

Hence ∠3 = ∠4 → (2) and ∠1 = ∠2 → (3)

Consider, ∠A = ∠3 + ∠4

= ∠4 + ∠4 [From (2)]

= 2∠4

= 2∠1

= ∠1 + ∠2

= ∠C

Therefore, ∠A = ∠C

Similarly, we can prove ∠B = ∠D