Question

Proove that
In parallelogram opposite angles are equal

Answer 1

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

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