Question

$ABC$ is an isosceles triangle with $AB=AC$ and $AD$ is altitude, then, ________ .

• A. $\angle B>\angle C$
• B. $\angle B<\angle C$
• C. $\angle B=\angle C$
• D. None of these

Answer 1

Answer: (C)

$\angle B=\angle C$

In the given triangle $\Delta ABC$:

$AB=AC$

$AD$ is perpendicular

So in $\Delta ADC,\Delta ADB$

$AD=ADCommon$

$\Delta ADC=\Delta ADB={90}^0$

$AC=ABGiven$

So By $RHS$ Congurence

$\Delta ADC\cong \Delta ADB$

$⟹\angle B=\angle C$.