Question

In the quadrilateral $ABCD,AD=CD$ and $\angle A={90}^o=\angle C$, prove that $AB=BC$.

Answer 1

Reference to the image above,

In $△ABD$ & $△BCD$

$AD=CD$ (Given... height)

$BC=BC$ (Common... Hypotenuse)

$\angle BAD=\angle BCD$ (right angles)

$\therefore △BAD\cong △BCD$ (By RHS congruency Rule)

$\therefore AB=BC$ ( By CPCT)