Question

$ABCD$ is a rectangle $AC$ is diagonal. Find the angles of $△ACD$. Give reasons

Answer 1

Given, $ABCD$ is a rectangle $AC$ is diagonal

Then $AD=BC$ and $AB=CD$

And $\angle ABC=\angle BCD=\angle CDA=\angle DAB={90}^0$

In $\Delta ABC$ and $\Delta ADC$

$\angle ABC=\angle ADC$ (Angle of rectangle)

$AB=DC$ (Opposite side of rectangle )

$AC=AC$ (Common side)

$\therefore \Delta ABC\cong \Delta ADC$

$\therefore \angle ACD=\angle ACB$

$\because \angle ACD+\angle ACB={90}^0$ ..........[Angle ACB is the angle of rectangle]

$\therefore 2\angle ACD={90}^0$ $\because \angle ACB=\angle ACD$

$\Rightarrow \angle ACD={45}^0$