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.
Q-4 BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles
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.
Q-5 ABC is an isosceles triangle with . Draw to show that
Given, In (AP is altitude) (Given) (Common line)
Therefore, by Right Angle-Hypostenuse-Side congruence condition.
Thus, (by Corresponding Parts of Congruent Triangles)