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

Isoceles Triangle

Give isoceles triangle of ABC

Give Isoceles Triangle

Give isoceles triangle of ABC

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.

Give ABC is an isosceles triangle in altitudes BE and CF are drawn to equal sides AC and AB respectivily

Give ABC Is an Isosceles Triangle

Give ABC is an isosceles triangle in altitudes BE and CF are drawn to equal sides AC and AB respectivily

Solution:

Given,BE and CF are altitudes.

AC=AB

  • To show, BE=CF

  • Proof,In ΔAEB and ΔAFC, A=A (Common) AEB=AFC (Right angles) AB=AC (Given)

  • Therefore, ΔAEBΔAFC (By AAS congruence condition).

  • Thus, BE=CF (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) ΔABEΔACF (ii) AB=AC , 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

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

Solution:

Given, BE=CF

  1. In ΔABE ΔACF , A=A (Common) AEB=AFC (Right angles) BE=CF (Given)Therefore, ΔABEΔACF (By AAS congruence condition).

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

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