Question

Show that:

A diagonal divides a parallelogram into two triangles of equal area.

Answer 1

Suppose ABCD is a parallelogram    ...(given)

Consider the triangles ABC and ADC:

AB = CD           ......[ABCD is a parallelogram]

AD  = BC        ......[ABCD is a parallelogram]

AC = AC          .....[Common]

By Side- Side -Side criterion of congruence, we have,

ΔABC ≅ ΔADC

Area of congruent triangles are equal.

Therefore, Area of ABC = Area of ADC