Question

prove that in a parallelogram ABCD are equal​

Answer 1

If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Answer 2

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).