Question

State True or False:
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 (OY is the angle bisector of $\angle$XYZ

So, PY = PO.

Now, $\angle$XYZ $<$ ${90}^{\circ }$

$\Rightarrow$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.