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BP=PC ,CQ=DQ, AP and AQ bisects angle BAC and CAD respectively. Prove that: 1)∆ABD is an isosceles ∆. 2)PQ//BD Refer to the question attached in the image.

BP=PC ,CQ=DQ, AP and AQ bisects angle BAC and CAD respectively.
Prove that:
1)∆ABD is an isosceles ∆.
2)PQ//BD
Refer to the question attached in the image.

Question Image
Grade:10

1 Answers

ROSHAN MUJEEB
askIITians Faculty 829 Points
2 years ago
Dear Student
Triangle ABC is isosceles because BP=PC and AP is angular bisector , so AB=AC
Similarly Triangle ADC is isosceles because AD=AC. so AB=AD therefore ABD is isosceles
Trinagle BDC is similar to triangle PQC by similarity criterion.

So BD and PQ are inclined at same angle

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