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NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.2 β Part 2
Isosceles Triangle
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.
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.
Solution:
Given,
- In ,
(Common)
(Right angles)
(Given)
Therefore, (By AAS congruence condition) .
- Thus, (By Corresponding Part of Congruent Triangle) and therefore ABC is an isosceles triangle.