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Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, prove that: AB/PQ = AD/PM.
Triangle ABC is similar to triangle PQR. If AD and PM are altitudes of the two triangles, 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 AD and PM are altitudes of the two triangles, prove that: AB/PQ = AD/PM.

Selina Solutions Concise Class 10 Maths Chapter 15 ex. 15(E) - 5

Solution:

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

So,

\[\angle ABC\text{ }=\angle PQR\]

i.e. \[\angle ABD\text{ }=\angle PQM\]

Also, \[\angle ADB\text{ }=\angle PMQ\][Both are right angles]

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

Thus,

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

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