The Pythagorean Theorem is probably the most famous mathematical relationship. In a right triangle, the sum of the squares of the lengths of the legs equals.

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The Pythagorean Theorem

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Presentation transcript:

The Pythagorean Theorem is probably the most famous mathematical relationship. In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

A set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2 is called a Pythagorean triple.

Example 1: Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form.

Example 2A: Crafts Application Randy is building a rectangular picture frame. He wants the ratio of the length to the width to be 3:1 and the diagonal to be 12 centimeters. How wide should the frame be? Round to the nearest tenth of a centimeter.

Check It Out! Example 2B What if...? According to the recommended safety ratio of 4:1, how high will a 30-foot ladder reach when placed against a wall? Round to the nearest inch.

Example 3A: Identifying Pythagorean Triples Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

Example 3B: Identifying Pythagorean Triples Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.

The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths.

You can also use side lengths to classify a triangle as acute or obtuse.

To understand why the Pythagorean inequalities are true, consider ∆ABC.

Example 4A/B: Classifying Triangles Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10 Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 8, 17

Lesson Quiz: Part I

Lesson Quiz: Part II 2. Find the value of x. 3. An entertainment center is 52 in. wide and 40 in. high. Will a TV with a 60 in. diagonal fit in it? Explain.

Lesson Quiz: Part III 4. What type of triangle could you form with sides of length 4”, 7” and 12” ? NOT a Triangle 5. Tell if the measures 7”, 11”, and 15” can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 72 + 112 < 152 OBTUSE

Lesson Quiz: Part IV 6. Given two legs of a Rt triangle are 4 and 8 Find the length of the hypotenuse in reduced radical form (RRF)