Question

$ABCD$ is a square and $BD$ is the diagonal. Find the measure of the area of $△ABD$.

Answer 1

In $△ABD$ and $△BCD$,

$AB=CD\left(\text{Each sides of a square are equal}\right)$

$\angle BAD=\angle BCD\left(\text{Each}90°\right)$

$AD=BC\left(\text{Each side of a square are equal}\right)$

$\therefore △ABD\cong △BCD\left(\text{By SAS}\right)$

Therefore,

$ar\left(△ABD\right)=ar\left(△BCD\right)\left(\text{Congruent triangles}\right)$

Therefore,

Area of square $=ar\left(△ABD\right)+ar\left(△BCD\right)$

$\Rightarrow 2ar\left(△ABD\right)=$ Area of square

$\Rightarrow ar\left(△ABD\right)=\frac{1}{2}$ Area of square