Question

State true or false:

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

• A. True
• B. False

Answer 1

The correct option is A True

Since ABCD is a parallelogram.
$AB\parallel CD$ and BD is a transversal
In $△ABD$ and $△DCB$
$\angle ABD=\angle CBD$(alternate interior angles)
AB=CD(opposite sides of a parallelogram)
AD=CB(opposite sides of a parallelogram)
BD=DB(common)
$\angle ABD\cong \angle DCB$ (By SAS)
$\therefore$ diagonal BD divides a parallelogram ABCD into two congruent triangles ABD and DCB.
Similarly diagonal AC divides parallelogram ABCD into two congruent triangles ABC and ADC.
Hence the diagonal divides a parallelogram into two triangles of equal areas.