Question
$ABC$ is a right angled triangle in which $\angle\text{A}=90^\circ$ and $\text{AB}=\text{AC}.$ and $\angle\text{B}$ and $\angle\text{C}.$
✓
Answer
Given that $ABC$ is a right angled triangle such that $\angle\text{A}=90^\circ$ and $\text{AB}=\text{AC}$
since, $\text{AB}=\text{AC}$
$\triangle\text{ABC}$ is also isosceles.
Therefore, we can say that $\triangle\text{ABC}$ is right angled isosceles triangle.
$\angle\text{C}=\angle\text{B}$ and $\angle\text{A}=90^\circ \ ...(\text{i)}$
Now, we have sum of angled in a triangle $= 180^\circ$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$90^\circ+\angle\text{B}+\angle\text{B}=180^\circ$ [From $(i)]$
$2\angle\text{B}=180^\circ-90^\circ$
$\angle\text{B}=45^\circ$
Therefore, $\angle\text{B}=\angle\text{C}=45^\circ$
since, $\text{AB}=\text{AC}$
$\triangle\text{ABC}$ is also isosceles.
Therefore, we can say that $\triangle\text{ABC}$ is right angled isosceles triangle.
$\angle\text{C}=\angle\text{B}$ and $\angle\text{A}=90^\circ \ ...(\text{i)}$
Now, we have sum of angled in a triangle $= 180^\circ$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$90^\circ+\angle\text{B}+\angle\text{B}=180^\circ$ [From $(i)]$
$2\angle\text{B}=180^\circ-90^\circ$
$\angle\text{B}=45^\circ$
Therefore, $\angle\text{B}=\angle\text{C}=45^\circ$
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