Question

O is a point on the bisector of an angle ABC. If the line through parallel to AB meets BC at P , prove that triangle BPO is issoceles.

Answer 1

Solution:-
BX is the bisector of ∠ ABC and O is a point of BX.
∴ ∠ ABO = ∠ OBP ....(1)
OP II AB
∴ ∠ ABO = ∠ BOP ...(2) [Alternate angles]
From (1) and (2), we get
∠ OBP = ∠ BOP
⇒ In Δ BPO,
PB = PO... [Sides opposite to equal angles are equal]
∴ Δ BPO is isosceles triangle.
Hence proved.