Find this important question of ncert class 9^{th} of chapter triangles .Sir please help me to find out the easiest and simplest solution of question 3 of exercise 7.2, give me the best solution of this question. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.

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# ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal. Q.3

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Solution:Given:

(i) BE and CF are altitudes.

(ii) AC = AB

To prove:BE = CF

Proof:Triangles ΔAEB and ΔAFC are similar by AAS congruency since

A = A (It is the common arm)

AEB = AFC (They are right angles)

AB = AC (Given in the question)

∴ ΔAEB ΔAFC and so, BE = CF (by CPCT).