Question

A diagonal of a paralleogram divides it into two congruent triangles.

• A. True
• B. False

Answer 1

The correct option is A True

Let us consider a parallelogram $ABCD$ with $AC$ as its diagonal.

To prove: $△ABC\cong △ADC$

Proof:

We know that the opposite sides of a parallelogram are parallel.

Hence $AB\parallel DC$ and $AD\parallel BC$

$AC$ is the transversal of the parallel lines $AB$ and $DC$

$\angle BAC=\angle DCA$ (Alternate angles) $...\left(1\right)$

$AC$ is the transversal of the parallel lines $AD$ and $BC$

$\angle DAC=\angle BCA$ $...\left(2\right)$

In $△ABC$ and $△ADC,$

$\angle BAC=\angle DCA$

$AC$ is the common side

$\angle DAC=\angle BCA$

Therefore, $△ABC\cong △ADC$