Question

In $△ABC,$ sides $ABandAC$ are of same length, and $AD$ is the angle bisector of $\angle A$. Select the appropriate option.

• A. $△ADB\cong △ACD$
• B. $△ABD\cong △ADC$
• C. $△ADB\cong △ADC$
• D. All of the above.

Answer 1

The correct option is C $△ADB\cong △ADC$


In above triangles $ADBandADC,$
$AB=AC$ [Given]
$\angle BAD=\angle CAD$
[$AD$ is the angular bisector of $\angle A$ ]
$AD=AD$ [Common side]

Hence, By S.A.S rule, $△ADB\cong △ADC$