Diagonal of parallelogram divide it into two congruent triangle

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. “

property of parallelogram

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

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.

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