# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Isosceles Triangle

An isosceles triangle is a triangle with (at least) two equal sides

Q-3 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) .

Q-4 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.