Question

In the given figure, If AB || DC and P is the midpoint of BD. Prove that P is also the midpoint of AC.

Answer 1

Given: AB DC, BP = DP

To Prove: CP = AP

Proof:

In :

∠A = ∠C (AB DC, AC is the transversal, ∠A and ∠C are alternate angles)

∠DPC = ∠APB (Vertically opposite angles)

DP = BP (Given)
(AAS congruency)

∴ CP = AP (Corresponding parts of congruent triangles)

Hence, P is the midpoint of AC.