Question

$ABCD$ is a rhombus . $AC$ is a diagonal. Is $\angle BAC\cong \angle DAC$? Give reason.

Answer 1

Given : $ABCD$ is a Rhombus

$\Rightarrow$ All sides are equal in length

$AB=BC=CD=DA\Rightarrow$ Opposite angles are equal while adjacent angles are Supplementary

$\angle DAB=\angle BCD,\angle ABC=\angle ADC$

$\Rightarrow$ diagonals bisect each other perpendicularly

In $△ABC$ and $\angle ADC,AB=CD$ (given)

$BC=AD$ (given)

$AC=AC$..... (common side)

$△ABC\cong △ADC$

$\angle BAC=\angle DAC$ (As $AC$ is a diagonal of Rhombus and diagonals bisect the angles.)