# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 3

Diagram of Isosceles Triangle: In Isosceles Triangle, the two sides are equal.

Q-5 ABC and DBC are two isosceles triangles on the same base BC (see Fig). Show that .

Solution:

Given,ABC and DBC are two isosceles triangles.

To show,

• Proof,In

(Common)

(ABC is an isosceles triangle.)

(BCD is an isosceles triangle.)

• Therefore, (By SSS congruence condition).

• Thus, (By Corresponding Part of Congruent Triangles).

Q-6 ΔABC is an isosceles triangle in which . Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that is a right angle.

Solution:

Given, and

• To show, is a right angle.

• Proof,In (Given) (Angles opposite to the equal sides are equal.)In , (Angles opposite to the equal sides are equal.)

• Now, In ,……………….equation(1)

• Similarly in , ……….equation(2)also, (BD is a straight line.)