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  • P is a point on the bisector of angle ABC. If the line through P, parallel to BA meets BC at Q, prove that BPQ is an isosceles triangle.

P is a point on the bisector of \angleABC. If the line through P, parallel to BA meets BC at Q, prove that BPQ is an isosceles triangle.

Answers (1)

Given : P is a point on the bisector \angleABC.

To prove:- BPQ is on an isosceles triangle

\angle1 = \angle2          (\because BP is bisector of \angleABC)

\angle1 = \angle3          (\because PQ is parallel to BA)

\therefore\angle2 = \angle3

\Rightarrow PQ = BQ (If two angles are equal their opposite sides are also equal)

\Rightarrow \trianglePBQ is on the isosceles triangle.

Hence proved.

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infoexpert24

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