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**Unit 6 Lesson 3 The Pythagorean Converse**

CCSS Lesson Goals G-SRT 4: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Apply the Pythagorean Converse to classify a triangle according to angle measure. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

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Draw In the Column Q’s section of your notes, attempt to draw a triangle with 1,1,and 3 cm sides. Then attempt to draw one with 4,4, and 3 cm sides Then attempt to draw one with 3,3, and 5 cm sides. Analyze and compare their differences with a student next to you.

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**Theorem Triangle Inequality Theorem**

The length of the longest side of a triangle must be less than the sum of the lengths of the two shorter sides. A B C B A C B C

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You Try Can a triangle be constructed with sides of the following measures? 5, 7, 8 8 < 5 + 7 Yes The length of the longest of a triangle must be less than the sum of the lengths of the two shorter sides.

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You Try Can a triangle be constructed with sides of the following measures? 4.2, 4.2, 8.4 < NO The length of the longest of a triangle must be less than the sum of the lengths of the two shorter sides.

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You Try Can a triangle be constructed with sides of the following measures? 3, 6, 10 10 < 3 + 6 NO

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You Try Can a triangle be constructed with sides of the following measures? 3, 3, 8 8 < 3 + 3 NO

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You try Can a triangle be constructed with sides of the following measures? 9, 5, 11 11 < 9 + 5 Yes

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**Theorem The Pythagorean Converse Keep the longest length on the left!**

A triangle can be classified according to angles measurement by comparing the square of the longest side of the triangle to the sum of the squares of the other two sides Keep the longest length on the left!

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example Classify the triangle as right, acute, or obtuse. 8 7 right

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**example obtuse Classify the triangle as right, acute, or obtuse. 13 10**

7 obtuse

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example Decide whether the set of numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. 8, 18, and 24 To be a triangle, the longest side must be less than the sum of other two sides.

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example Decide whether the set of numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse. 8, 18, and 24 Use the Pythagorean Converse to classify the triangle. obtuse

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You Try Decide whether the set of numbers can represent the side lengths of a triangle. 32, 48, and 51 To be a triangle, the longest side must be less than the sum of other two sides.

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You Try Classify the triangle as right, acute, or obtuse. 32, 48, and 51 Use the Pythagorean Converse to classify the triangle. acute

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You Try Decide whether the set of numbers can represent the side lengths of a triangle. 8, 40, 41 obtuse

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You Try Decide whether the set of numbers can represent the side lengths of a triangle. 12.3, 16.4, 20.5 right

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example Find the range of values for c, the longest side of the triangle, so that the triangle is acute when a = 8 and b = 14. 8 c 14 A B C 16.1

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example Find the range of values for c, the longest side of the triangle, so that the triangle is obtuse when a = 12 and b = 15. 12 c 15 A B C 19.2

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You Try Find the range of values for c, the longest side of the triangle, so that the triangle is obtuse when a = 7 and b = 16. 7 c 16 A B C 17.5

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Example B Obtuse Triangle C A

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Summary Create an acronym, poem, or mnemonic to help you remember the Pythagorean Converse.

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**Today’s Assignment p. 546: 14 – 20 e; 32, 33, 34 +**

Find the value for c, the longest side of the triangle, so that the triangle is a) acute and b) obtuse. 5, 11 12, 17

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Find the value for c, the longest side of the triangle, so that the triangle is a) acute and b) obtuse. +1) 5, 11 +2) 12, 17

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