NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 3
Altitude of triangle
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude.
Q4 BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles
Solution:
Given,BE and CF are two equal altitudes.

In and , (Altitudes) (Common) (Common)

Therefore, by RHS congruence condition.

Now, (by Corresponding Parts of Congruent Triangles)Thus, as sides opposite to the equal angles are equal.
Q5 ABC is an isosceles triangle with . Draw to show that
Solution:

Given, In (AP is altitude) (Given) (Common line)

Therefore, by Right AngleHypostenuseSide congruence condition.

Thus, (by Corresponding Parts of Congruent Triangles)