Question

The diagonal of a parallelogram divides it into 2 congruent triangles. State whether true or false.

• A. True
• B. False

Answer 1

The correct option is

A

True

In parallelogram ABCD, diagonal BD divides it into 2 equal triangle.

Since ABCD is a parallelogram, the opposite sides are equal.

Therefore, AB = CD and AD = BC.

In triangles ABD and CBD

AB = CD (Opposite sides of a parallelogram)

AD = BC (Opposite sides of a parallelogram)

BD = BD ( common)

Thus, by SSS congruency condition. $△$ ABD $\cong$ $△$ CBD.

Therefore, we can say that the diagonal of a parallelogram divides it into 2 congruent triangles.

Hence, option (A) is correct.