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.