Question

Theorem 8.2 : In a parallelogram, opposite sides are equal.
pls prove this theoram​

Answer 1

Step-by-step explanation:

ABCD is a parallelogram.

To prove that AB = CD and AD = BC.

Join the diagonal AC.

In the triangles ABC and CDA:

angleBAC = angleDCA (alternate angles, AB || DC)

angleBCA = angleDAC (alternate angles, AD || BC)

AC = CA (common)

so triangleABC ≡ triangleCDA (AAS)

Hence AB = CD and BC = AD (matching sides of congruent triangles).

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