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Home >> Triangle >> Properties >> Pythagoras Theorem >>

## Define Pythagoras Theorem

 Sum of Two Sides Angle Sum Property Angles opposite to equal sides of triangle are equal Angle opposite to longer side is greater Pythagoras Theorem Exterior Angle Property of a Triangle Mid point property of Triangle Triangles on same base & between same parallel lines

Before you study Pythagoras theorem, you are advised to study:

What is Right Angle Triangle ?

Pythagoras was a Greek philosopher of 6th century B.C. who had given a theorem used in right-angles triangle and hence this theorem was named after him and called as Pythagoras Theorem.

Pythagoras Property or Pythagoras Theorem says that "The Square of the Hypotenuse of a Right Angle Triangle is Equals to the Sum of Squares of its Legs"

In short we can write it as:
(Hypotenuse)2 = (Leg 1)2 + (Leg 2)2

Since legs are the other two sides of right angle triangle, so we can also write it as:
(Hypotenuse)2 = (Side 1)2 + (side 2)2

Example: In the following figure of △ ABC: right angled at B:

Leg 1 = AB = 5 cm
Leg 2 = BC = 12 cm
And we have to find hypotenuse i.e. AC ?

Apply Pythagoras Theorem and we get:
(Hypotenuse)2 = (Leg 1)2 + (Leg 2)2

Or we can also write it as:
(AC)2 = (AB)2 + (BC)2

Put the values of leg 1 and leg 2 from above and we get
(AC)2 = (5)2 + (12)2

Solve brackets on R.H.S and we get:
(AC)2 = 25 + 144

Solve addition expression on R.H.S. and we get:
(AC)2 = 169

Take square root of both sides and we get:
AC = 13

Hence, hypotenuse = 13 cm

Since, you have learn that Pythagoras Theorem applies to right angle triangle only, so this also concludes that:
In a triangle, if Pythagoras theorem hold true then triangle must be Right Angle Triangle

Here, you must also note that Hypotenuse is the Longest Side in Right Angle Triangle.

### Study More Solved Questions / Examples

 In a triangle, hypotenuse is 10 cm and one of its legs is 6 cm. Find the length of other leg of the triangle. Length of three sides of a triangle are 10 cm, 24 cm and 26 cm. check whether this triangle is a right angle triangle ? In the following diagram, AB = AD = 5 cm, AC = 4 cm, find BD. A man uses a 37 m long ladder to reach the 35 m high roof of his house, placing its one end on the ground and other against the roof end. Ladder, one end on the ground, is placed at a 'X' distance from foot of the house. Find this 'X' distance.

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