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
∠ 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 rightangled.
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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 rightangled.
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