Question

Prove that the opposite sides of a parallelogram are equal.

Answer 1

Let ABCD be a parallelogram and AC be a diagonal. Observe that the diagonal AC divides parallelogram ABCD into two triangles, namely, ∆ABC and ∆CDA. We need to first prove that these triangles are congruent.

In ∆ABC and ∆CDA; note that BC || Ad and AC is a transversal.

So, BCA = DAC (Pair of alternate angles)

And AC = CA (common)

So, ∆ABC and ∆CDA are congruent (ASA rule).

Therefore, the corresponding parts AB = CD and AD = Bc.

Hence proved.