Question

Show that diagonal of parallelogram divides it into two congruent triangles.

Answer 1

Given:

A Parallelogram ABCD and AC is its diagonal.

To prove: $∆\mathrm{ABC}\cong ∆\mathrm{ADC}$

Proof: In $∆\mathrm{ABC}$ and $∆\mathrm{ADC}$

$\mathrm{AB}=\mathrm{CD}$ (opposite sides of parallelogram are equal)

$\angle \mathrm{ABC}=\angle \mathrm{ADC}$ (opposite angles of parallelogram are equal)

$\mathrm{BC}=\mathrm{AD}$ (opposite sides of parallelogram are equal)

⇒$∆\mathrm{ABC}\cong ∆\mathrm{ADC}$ by SAS rule

Thus, diagonal of parallelogram divides it into two congruent triangles.