NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.3 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Altitude of triangle

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

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

  • Therefore, by Right Angle-Hypostenuse-Side congruence condition.
  • Thus, (by Corresponding Parts of Congruent Triangles)