The Pythagorean Theorem

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The Pythagorean Theorem

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Presentation transcript:

The Pythagorean Theorem 5-7 The Pythagorean Theorem Section 5.7 Holt McDougal Geometry Holt Geometry

Warm Up Classify each triangle by its angle measures. 1. 2. 3. Simplify 4. If a = 6, b = 7, and c = 12, find a2 + b2 and find c2. Which value is greater?

The Pythagorean Theorem is probably the most famous mathematical relationship. It states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. a2 + b2 = c2

Find the value of x. Give your answer in simplest radical form.

Find the value of x. Give your answer in simplest radical form.

Find the value of x. Give your answer in simplest radical form.

Find the value of x. Give your answer in simplest radical form.

Randy is building a rectangular picture frame 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.

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.

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

Tell if the side lengths form a Pythagorean triple.. Find the missing side length.

Tell if the side lengths form a Pythagorean triple.. Find the missing side length.

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.

By the Triangle Inequality Theorem, the sum of any two side lengths of a triangle is greater than the third side length. Remember!

Tell if the measures can be the side lengths of a triangle Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. a. 5, 7, 10 b. 5, 8, 17 c. 7, 12, 16 d. 3.8, 4.1, 5.2

Lesson Quiz: Part I 1. Find the value of x. 2. 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 II 3. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. 4. 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.