Mathematics
Triangle ABC is similar to triangle PQR. If bisector of angle BAC meets BC at point D and bisector of angle QPR meets QR at point M, prove that: .
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Answer
Given, ∆ABC ~ ∆PQR and AD and PM are the angle bisectors.
So,
⇒ ∠A = ∠P
⇒
⇒ ∠BAD = ∠QPM
Also, ∠ABC = ∠PQR i.e., ∠ABD = ∠PQM.
∴ ∆ABD ~ ∆PQM [By AA]
Since, corresponding sides of similar triangles are proportional.
.
Hence, proved that .
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