This is very important question of ncert class 9th of chapter triangles. How I solve the best solution of exercise 7.1 question number 3. Please help me to solve this in a easy and best way. Find 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.
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).