MCQ
$ABC$ is an isosceles triangle with $AB = AC$ and $AD$ is altitude, then ____.
- A$\angle\text{B}>\angle\text{C}$
- B$\angle\text{B}<\angle\text{C}$
- ✓$\angle\text{B}=\angle\text{C}$
- D$\text{None of these}$
✓
Answer
Correct option: C.
$\angle\text{B}=\angle\text{C}$
In the given triangle $\triangle\text{ABC}$
$AB = AC$
$AD$ is perpendicular
So in $\triangle\text{ADC},\triangle\text{ADB}$
$AD = AD$ Common
$\triangle\text{ADC}=\triangle\text{ADB}=90^\circ$
$\triangle\text{ADC}\cong\triangle\text{ADB}$
$\Rightarrow\angle\text{B}=\angle\text{C}$
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