Question

$ABCD$ is a rectangle, $AC$ and $BD$ are diagonals. Prove that diagonals are equal.

Answer 1

Step $1:$ Drawing the diagram:

$ABCD$ is a rectangle.

Join the diagonals $AC$ and $BD$.

Step $2:$ Proving the diagonals are equal:

In $\Delta ABC$ and $\Delta BAD$ ,

$AB=BA$ (common side)

$\angle ABC=\angle BAD=90°$ {right angles}

$BC=AD$ [Opposite sides of rectangle are equal]

Therefore, By SAS congruence criteria,

$\Delta ABC\cong \Delta BAD$

Therefore, By CPCT,

$AC=BD$

Hence proved.