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Question
Show that:
A diagonal divides a parallelogram into two triangles of equal area.
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Solution
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
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