Question

Prove that a rhombus with one angle ${90}^{\circ }$ is a square.

Answer 1

Consider the 2 properties of Rhombus

$\left(1\right)$ Opposite angles are equal

$\left(2\right)$ Adjacent Angle sum is ${180}^{\circ }$

Let us consider $ABCD$ as Rhombus

Let $\angle A$ be ${90}^{\circ }$

By property $\left(1\right)$ $\angle C={90}^{\circ }$

By property $\left(2\right)$ $\angle B,\angle D={90}^{\circ }$