Question
O is any point on the bisector of the acute angle ∠XYZ. From O, a line is extended to join XY such that OP is parallel to ZY. Then, △YPO is:
Answer: Option B
:
B
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B
∠ POY = ∠ OYZ (alternate angles)
∠Y is bisected, so ∠ POY = ∠ PYO
Hence, PY = PO
So, △YPO is isosceles
Also, it is given that ∠XYZ is acute, so any angle which is half of it (bisected by OY) is less than 45∘.
or ∠ PYO + ∠OYZ < 90∘
Hence, the third angle of the △YPO i.e. ∠ YPO will be obtuse to satisfy angle-sum property of a triangle.
Hence, △YPO is isosceles but not right angled.
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