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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: AB/PQ = AD/PM
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: AB/PQ = AD/PM
Class 10 | Exercise 15E | ICSE | Maths | Selina | Similarity (With Applications to Maps and Models)
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: AB/PQ = AD/PM

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(E) - 6

Solution:

According to the given question, \[\vartriangle ABC\text{ }\sim\text{ }\vartriangle PQR\]

And, \[AD\text{ }and\text{ }PM\]are the angle bisectors.

So,

\[\angle BAD\text{ }=\angle QPM\]

Also, \[\angle ABC\text{ }=\angle PQR\text{ }i.e.\angle ABD\text{ }=\angle PQM\]

Hence\[\text{ }\vartriangle ABD\text{ }\sim\text{ }\vartriangle PQM\text{ }by\text{ }AA\] criterion for similarity.

Thus,

\[AB/PQ\text{ }=\text{ }AD/PM\]

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