Question

Show that a diagonal divides a parallelogram into two triangles of equal area.

Answer 1

Let $ABCD$ be a parallelogram and $BD$ is one of its diagonal. As we know that the opposite sides of a parallelogram are equal.

$\therefore AB=CD$ and $AD=BC$

In $△ABD$ and $△CDB$,

$AB=CD,AD=BC$ [given]

$BD=BD$ [common]

$\therefore △ABD\cong △ADC$

$\Rightarrow ar\left(△ABD\right)=ar\left(△CBD\right)$

$\Rightarrow ar\left(△ABC\right)=ar\left(△CDA\right)$

i.e congruent triangles have equal area