The Pythagoras Theorem c a a2 + b2 = c2 b.

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Presentation transcript:

The Pythagoras Theorem c a a2 + b2 = c2 b

This is a right triangle:

We call it a right triangle because it contains a right angle.

The measure of a right angle is 90o

The little square in a triangle tells you it is a right angle.

About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.

Pythagoras realized that if you have a right triangle, 3 4 5

and you square the lengths of the two sides that make up the right angle, 3 4 5

and add them together, 3 4 5

you get the same number you would get by squaring the other side. 3 4 5

Pythagoras Theorem states that The square of the length of the hypotenuse of a right triangle is the sum of the squares of the lengths of the two sides. a b c Hypotenuse Hypotenuse is located opposite to the right angle in the triangle

The 3 numbers which are satisfying the Pythagoras theorem are called the Pythagorean Triplets and can form right triangle using the given sides. We can also say given 3 numbers are pythagorean triplets if sum of square of two smallest numbers is equal to third number.

Example1 : Do the Numbers 11, 12 and 5 form a Pythagorean Triplet? Solution: If sum of square of two smaller numbers = square of third number then the numbers form Pythagorean Triplet Sum of square of two smaller numbers = 52 + 112 = 121 + 25 = 146 Square of third number = 122 = 144 Ans:- Since sum of square of two small number is not equal to square of third number therefore the numbers 11,12 and 5 does not form a Pythagorean Triplet.

Example 2: Check whether the following can be the sides of a right angled triangle AB = 6 cm, BC = 8 cm, AC = 10cm. Solution If sum of square of two smaller sides = square of third side then the numbers form Pythagorean Triplet Sum of square of two smaller sides = 62 + 82 = 36 + 64 = 100 Square of third side = 102 = 100 Ans:- Since sum of square of two smaller side is equal to square of third side therefore we can form triangle from the given sides.

Try These Check whether the following can be the sides of a right angled triangle AB = 12 cm, BC = 14 cm, AC = 15cm. Do the numbers 5, 6 and 7 form a Pythagorean Triplet?