Question

Prove that, opposite sides of a parallelogram are equal.

Answer 1

R.E.F image

In triangle ADC and ABC,

$\angle DAC=\angle ACB(AB\parallel CD$ and taking AC as transversal)

$AC=AC$ (common)

$\angle DCA=\angle BAC(AB\parallel CD$ taking AC as transversal)

By ASA criterion of concurrency triangle ADC is congruent to triangle ABC.

$AD=BC$ (By CPCT)

$AB=CD$ (By CPCT)