### Mathematics Class VII

Integers
Fractions and Decimals
Exponents and Powers
Algebraic Equations
Simple Linear Equations
Lines and Angles
Comparing Quantities
Congruence of Triangles
Rational Numbers
Perimeter and Area
Data Handling
Practical Geometry
Symmetry
Visualising Solid Shapes

# Right-Angled Triangles And Pythagoras Property

##### Right Angled Triangle

A right-angled triangle is a triangle which has one of its angles as 90° and the side opposite to that angle is the largest leg of the triangle which is known as Hypotenuse .The other two sides are called Legs.

##### Pythagoras theorem

In a right angle triangle,

(Hypotenuse)2 = (base)2 + (height)2

The reverse of Pythagoras theorem is also applicable, i.e. if the Pythagoras property holds in a triangle then it must be a right-angled triangle.

Example

Find the value of x in the given triangle if the hypotenuse is 5 cm and height is 4 cm.

Solution

Given:

Hypotenuse = 5 cm

Height = 4 cm

Base = x cm

(Hypotenuse)2 = (base)2 + (height)2

52 = x2 + 42

x2 = 5– 42

x2 = 25 – 16

x = 9

x = 3 cm

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