Question

Prove that a diagonal of a parallelogram divides it into two congruent triangles.

Answer 1

Let $ABCD$ be a parallelogram and $AC$ be its diagonal.

Consider $\Delta ADC$ and $\Delta ABC$, such that,

$\angle DAC=\angle ACB$ [Pair of alternate angles as $DC\parallel AB$]

$\angle DCA=\angle ABC$ [Pair of alternate angles $DC\parallel AB$]

$AC=CA$ [Common side]

$\therefore \Delta ADC\cong \Delta CBA$ by ASA congruence rule

Hence,a diagonal of a parallelogram divides it into two congruent triangles.