Question

In the given figure, $\angle ACB=90°,\angle ACD=90°$ and $\overline{AB}=\overline{AD}$.

Therefore we can use ______________Congruence rule. $\left[RHS/ASA\right]$

$△ABC\cong \_\_\_\_\_\_\_\_\_.\left[△ADC/△DCA\right]$

• A. $RHS$
• B. $△ADC$

Answer 1

Step-1 :RHS Criterion:

Two right-angled triangles are congruent if the hypotenuse and a leg of one triangle are equal to the hypotenuse and the corresponding leg of the other. This condition is called the RHS criterion.

Here $\angle ACB=90°,\angle ACD=90°$ and $\overline{AB}=\overline{AD}$.

$AC=AC$

Therefore, we can use the $RHS$ Congruence rule.

Step-2 Congruent triangle:

$\angle ACB=90°,\angle ACD=90°$and $\overline{AB}=\overline{AD}$

$AC=AC$

$△ABC\cong △ADC$ [by $RHS$]

Hence,$△ABC\cong △ADC$