Question

A diagonal of a parallelogram divides it into :

• A. two congruent triangles
• B. two equilateral triangles
• C. two isosceles triangle
• D. None of the above

Answer 1

The correct option is A

two congruent triangles

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

Proof - In a parallelogram $ABCD$, AB$\parallel$CD and BC$\parallel$AD.
AC is the transversal for the parallel pair of lines.
In $△$ ABC and $△$ ADC :
$\angle$ ACB = $\angle$ CAD (alternate interior angles)
$\angle$ BAC = $\angle$ DCA (alternate interior angles)
$AC=CA$
$\Rightarrow$ $△$ ABC $\cong$ $△$ ADC. ( ASA congruency )
Hence proved.