NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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

Give Isoceles Triangle That Two Side Are Same

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

ABC and DBC Are Two Isosceles Triangles

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.

Triangle ABC is Isosceles

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)