P is a point on the bisector of `angle ABC ` .If the line through P,parallel to BA meet at Q ,prove that BPO is an isosceles triangle.

Explanation

Given we have P is a point on the bisector of `angle ABC` and draw the line through P parallel to BA and meet BC at Q .

To prove `Delta BPQ ` is an isosceles triangle .
Proof ` angle1= angle2 ` [`because ` BP is bisector of `angle B `(given )]
Now `angle1=angle3` [alternate interior angles as ` PQ abs()` AB ]
`thefore " " angle 2 = angle 3 `
`rArr " " PQ =BQ " " `[sides opposite to equal angles are equal ]
Hence `Delta BPQ` is an isosceles triangle.