Exploring

Pythagorean Theorem

 

For any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the legs.

Note: The hypotenuse is always the longest side of a right triangle.

 We can verify if a triangle is a right triangle by checking if this equation is satisfied.

The Pythagorean Theorem                                                                                                          

Example 1: Determine whether a triangle with side lengths 5 cm, 9 cm, and 6 cm is a right triangle.

c = longest side = 9 cm a and b = legs = 5 cm and 6 cm

a2 + b2 c2 = 52 + 62 = 92

= 25 + 36 = 81= 61 = 81

Since 61 ≠ 81, the Pythagorean theorem is not satisfied, so the triangle is not a right triangle.

If it were a right triangle, then a2 + b2 would give the same number as c2.

The Pythagorean Theorem                                                                                                          

Example 2: Determine whether a triangle with side lengths 11, 61, 60 is a right triangle.

c = longest side = 61 cm a and b = legs = 11 cm and 60 cm

a2 + b2 c2 = 112 + 602 = 612

= 121 + 3600 = 3721= 3721 = 3721

Since 3721 = 3721, the Pythagorean theorem is satisfied, so the triangle is a right triangle.

A set of three whole numbers that satisfies the Pythagorean Theorem is called a Pythagorean triple.

Classwork                                                                                                          

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