NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 3
Diagram of Isosceles Triangle: In Isosceles Triangle, the two sides are equal.
Q5 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).
Q6 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.)

Adding (i) and (ii)