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

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

Give Isoceles Triangle that two side are same

Give Isoceles Triangle

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

ABC and DBC are two isosceles triangles on same base BC

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

Triangle ABC is isosceles AB=AC, Side BA is produced to D such that AD = AB

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)