NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.4 – Part 1

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Hypotenuse triangle

Give hypotenuse triangle Mq is hypotenuse

Give Hypotenuse Triangle

Give hypotenuse triangle Mq is hypotenuse

The length of the hypotenuse of a right triangle can be found using the Pythagorean Theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

1. Show that in a right angled triangle, the hypotenuse is the longest side.

Solution:

Give right angle ABC, it 's hypotenuse is the longest side

Give Right Angle ABC

Give right angle ABC, it 's hypotenuse is the longest side

Give , ABC is a triangle right angled at B.

  • Now,

    A+B+C=180° A+C=90° and Bis90° . ( ABC is a triangle right angled at B)

  • Since, B is the largest angle of the triangle, the side opposite to it must be the largest.

  • So, BC is the hypotenuse which is the largest side of the right angled triangle ABC.

Q-2 In the figure, sides AB and AC of ΔABC are extended to points P and Q respectively. Also, PBC<QCB . Show that AC>AB .

Give side AB and AC of ΔABC it are extended to point P and Q respectively.and ∠PBC < ∠QCB

Give Side AB and AC of ΔABC

Give side AB and AC of ΔABC it are extended to point P and Q respectively.and ∠PBC < ∠QCB

Solution:

Given, PBC<QCB

  • Now,

    ABC+PBC=180°ABC=180°PBC

  • also,

    ACB+QCB=180° ACB=180°QCB

  • Since, PBC<QCB therefore, ABC>ACB

  • Thus, AC>AB as sides opposite to the larger angle is larger.

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