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.