NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.5

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NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties Exercise 6.5 is given in the pdf format below. Exercise 6.5 discusses two very important properties of triangles:

In a right-angled triangle, the side opposite to the right angle is termed the hypotenuse and the other two sides are called its legs. The Pythagoras property is a property applied to right-angled triangles. It states that in a right-angled triangle,

The square on the hypotenuse = the sum of the squares on its legs

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Example From Class 7 Chapter 6 The Triangle and its Properties

Ques. Verify Pythagoras theorem for the following triangle ABC.

Verify Pythagoras theorem for the following triangle ABC

Ans. The Pythagoras theorem states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on its legs.

Therefore, in ∏ ABC,

AC is the hypotenuse = 13 cm,

BC is the base = 5 cm and

AB is the perpendicular = 12 cm

Applying Pythagoras theorem we get,

(AC)² = (AB)² + (BC)²

On LHS we get,

13² = 169

On RHS we get,

5²+ 12² = 25+ 144

=169

Therefore,

LHS=RHS

The Pythagoras theorem is hence proved.

Read More:

Triangles	Equilateral Triangle	Area of Isosceles Triangle
Properties of a Triangle	Isosceles Triangle Theorems	Isosceles Right Triangle
Isosceles Triangle	Sides of a Triangle	Similarity of Triangles

Class 7 Maths Important Links:

NCERT Solutions for Class 7 Maths	Maths MCQs	Maths Study Material
Maths Formulas	Triangles Important Questions	Difference Between in Maths
Triangle Theorems	Important Terms: Triangles	Perimeter of a Triangle
Congruence of Triangles	Area of Equilateral Triangle	Exterior Angle Theorem