In this chapter we will prove important theorem of parallelogram.

According to the theorem ” **the diagonal of parallelogram divides the figure into two congruent triangle**. “

Given above is parallelogram in which opposite sides are equal and parallel with AC as diagonal.

**To Prove:**

Prove that triangle ACD is congruent to triangle ACB.

\triangle ABC\ \cong \triangle ADC

**Proof:**

AB & CD are parallel lines with transversal AC.

∠BAC = ∠DCA ( alternate angles )

∠BCA = ∠DAC ( alternate angles )

**Now consider triangle ABC and ADC;**

∠BAC = ∠DCA ( alternate angles )

AB = CD ( opposite sides of parallelogram are equal )

∠BCA = ∠DAC ( alternate angles )

By ASA congruency, both the triangles are congruent.

Hence Proved.