NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 3

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Altitude of triangle

Give triangle of ABC, altibute is AB and base is BC

Give Altitude Triangle of ABC

Give triangle of ABC, altibute is AB and base is BC

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

Solution:

a Triangle ABC

A triangle ABC are two altitudes of BE and CF

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

Solution:

Isosceles Triangle ABC With AB=AC

Isosceles triangle ABC with AB=AC also AP ⊥ BC and ∠B = ∠C.

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

  • Therefore, by Right Angle-Hypostenuse-Side congruence condition.

  • Thus, (by Corresponding Parts of Congruent Triangles)