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Geometry 5.7. The Pythagorean Theorem. Learning Targets. Students will be able to… Use the Pythagorean theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles. Warm-up. Homework Check. Homework Check. Vocabulary. c. a. b. Right Triangles.
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Geometry 5.7 The Pythagorean Theorem
Learning Targets • Students will be able to… • Use the Pythagorean theorem and its converse to solve problems. • Use Pythagorean inequalities to classify triangles.
Vocabulary c a b
Right Triangles Hypotenuse – Always the longest side. - Side opposite the right angle. - Side c is the hypotenuse Pythagorean Theorem: c a b Leg – The two shorter sides. - The sides that make up the right angle. - a and b are the legs
Example Type 1: Using the Pythagorean Theorem Find the value of x
Example Type 1: Using the Pythagorean Theorem Find the value of x
Pythagorean Triples • Pythagorean Triples – all sides of the right triangle are whole numbers. • Still use the Pythagorean theorem to find the missing side. • However, when done if you notice that all three numbers are whole numbers then you have a Pythagorean triple. • 3, 4, 5 is a Pythagorean triple and any number times 3, 4, and 5 will create a Pythagorean triple.
Example 2: Identifying Pythagorean Triples • Find the missing side. Tell if the side lengths form a Pythagorean Triple
Example 2: Identifying Pythagorean Triples Find the missing side. Tell if the side lengths form a Pythagorean Triple
Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • Step 1: Determine if a triangle • Step 2: Classify the triangle • Classify the triangle using the following chart
Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • A. 8, 11, 13 B. 7, 12, 16
Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • C. 5.8, 9.3, 15.6 D. 3.8, 4.1, 5.2
Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • E. 5, 7, 10 F. 11, 18, 34