NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 – Part 2

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Isoceles Triangle

Give isoceles triangle of ABC

Give Isoceles Triangle

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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.

ABC is an Isosceles Triangle

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.

Give ABC is triangle BE and CF to sides AC and AB are equal

Give ABC is Triangle

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ABC is Triangle

Solution:

Given,

  1. In , (Common) (Right angles) (Given)Therefore, (By AAS congruence condition).

  2. Thus, (By Corresponding Part of Congruent Triangle) and therefore ABC is an isosceles triangle.