Section 8-1: The Pythagorean Theorem and its Converse.

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Presentation transcript:

Section 8-1: The Pythagorean Theorem and its Converse

To use the Pythagorean Theorem. To use the converse of the Pythagorean Theorem.

Pythagorean Triple

Greek mathematician from the 6 th century BC. Famous for the Pythagorean Theorem Others knew of the Pythagorean Theorem first: Babylonians Egyptians Chinese

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.

A Pythagorean triple is a set of nonzero whole numbers a, b, and c that satisfy the equation:

Solve for the variable. Do the sides of the triangle form a Pythagorean triple? x

Solve for the variable. Do the sides of the triangle form a Pythagorean triple? y

Solve for the variable. Do the sides of the triangle form a Pythagorean triple? 4 8 z

If the square of the lengths of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Is the triangle a right triangle?

Is the triangle a right triangle? 6 2 5

If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

7, 8, and 11 16, 19, and 24 5, 7, and 10