Question

O is any point on the bisector of the acute angle $\angle XYZ$. The line $OP\parallel ZY$. Then, $△YPO$ is an Isosceles right-angled triangle.

• A. Scalene
• B. Isosceles but not right angled

Answer 1

The correct option is B

Isosceles but not right angled

$\angle POY=\angle ZYO(alt.\angle s)=\angle PYO.$

So,$PY=PO.$

Now, $\angle XYZ<0^{\circ }$

$\Rightarrow POY<{45}^{\circ }\Rightarrow \angle PYO<{45}^{\circ }$

$\therefore \angle YPO>{90}^{\circ }$

Hence, $\Delta YPO$ is an isosceles but not a right angled triangle.