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:

Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [B, C] Segment h Segment h: Segment [C, A] A text1 = "A" B text2 = "B" C text3 = "C"

Right Angle ABC

Right angle ABC, its hypotenuse is the longest side

Give , ABC is a triangle right angled at B.

  • Now,

    Equation Equation and Equation . ( Equation 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 Equation are extended to points P and Q respectively. Also, Equation . Show that Equation .

Segment f Segment f: Segment [G, H] Vector u Vector u: Vector[A, B] Vector u Vector u: Vector[A, B] Vector v Vector v: Vector[E, F] Vector v Vector v: Vector[E, F] Point C Point C: Point on u Point C Point C: Point on u Point D Point D: Point on v Point D Point D: Point on v A text1 = "A" B text2 = "B" C text3 = "C" P text4 = "P" Q text5 = "Q"

Side AB and AC of ΔABC

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

Solution:

Given, Equation

  • Now,

    Equation

  • also,

    Equation Equation

  • Since, Equation therefore, Equation

  • Thus, Equation as sides opposite to the larger angle is larger.

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