NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 2
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Isoceles Triangle
An isosceles triangle is a triangle with (at least) two equal sides
Q3 ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig). Show that these altitudes are equal.
Solution:
Given,BE and CF are altitudes.

To show,

Proof,In and (Common) (Right angles) (Given)

Therefore, (By AAS congruence condition).

Thus, (By Corresponding Part Congruent Triangles).
Q4 ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that(i) (ii) , i.e., ABC is an isosceles triangle.
Solution:
Given,

In , (Common) (Right angles) (Given)Therefore, (By AAS congruence condition).

Thus, (By Corresponding Part of Congruent Triangle) and therefore ABC is an isosceles triangle.