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: .
Similarity
3 Likes
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 .
Answered By
1 Like
Related Questions
Triangle ABC is similar to triangle PQR. If AD and PM are corresponding medians of the two triangles, prove that: .
Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, prove that: .
In the following figure, ∠AXY = ∠AYX.
If , show that triangle ABC is isosceles.
In the following figure, DE || AC and DC || AP. Prove that : .
