8-1: The Pythagorean Theorem and its Converse

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Presentation transcript:

8-1: The Pythagorean Theorem and its Converse

The Pythagorean Theorem In words: As an equation:

Pythagorean Triples A set of nonzero whole numbers a, b, and c that satisfy the equation 𝑎 2 + 𝑏 2 = 𝑐 2 is called a Pythagorean triple Example: 3, 4, 5 or 8, 15, 17

Pythagorean Triples The length of the hypotenuse of a right triangle is 25 and one leg has a length of 10. Do the lengths of the sides form a Pythagorean triple? Do the sides of triangle ABC form a Pythagorean triple?

Converse of the Pythagorean Theorem Write the converse of the Pythagorean theorem:

Converse of the Pythagorean Theorem A triangle has sides of lengths 16, 48, and 50. Is it a right triangle? Is this triangle a right triangle?

Side Measures of Obtuse and Acute Triangles You will use GeoGebra to explore the measures of the side lengths of obtuse and acute triangles.

Your Rules: What is the rule for the relationship between obtuse triangles’ side lengths? What is the rule for the relationship between acute triangles’ side lengths?

Ticket out of class: Please put your name on your paper.

Ticket out of class: Find the value of x. Find the value of x. The lengths of the sides of a triangle are 5cm, 8cm, and 10cm. Is the triangle acute, right, or obtuse?