Question

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

• A. True
• B. False

Answer 1

The correct option is A

True

Suppose ABCD is a parallelogram and BD is the diagonal.
There are two triangles - $\Delta$ ABD and $\Delta$ CDB
In $\Delta$ ABD and $\Delta$ CDB,
AD = BC (opposite sides of a parallelogram are equal)
AB = CD (opposite sides of a parallelogram are equal)
BD is common
$\therefore$ By SSS criterion of congruency,
$\Delta$ ABD $\cong$ $\Delta$ CDB
Hence, the given statement is true.