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Published byMary Newton Modified over 6 years ago

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**Geometry Agenda 1. ENTRANCE 2. Go over Tests/Spiral**

The Pythagorean Theorem and its Converse Special Right Triangles 5. Practice Assignment 6. EXIT

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**Chapter 9 7-2 The Pythagorean Theorem and its Converse**

(We actually start with 2 sections of Chapter 7.) 7-2 The Pythagorean Theorem and its Converse 7-3 Special Right Triangles

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**Theorem 7-4 The Pythagorean Theorem**

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

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**Common Pythagorean Triples**

Certain sets of three numbers appear often in Geometry problems since they satisfy the Pythagorean Theorem. 3, 4, 5 5, 12, 13 Multiples of these triples 8, 15, 17 will work as well, such as 7, 24, , 8, 10 and 15, 36, 39. 9, 40, 41

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**Theorems 7-5, 7-6, and 7-7 Converse of the Pythagorean Theorem**

If , then the triangle is a right triangle. If , then the triangle is an obtuse triangle. If , then the triangle is an acute triangle.

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Example #1 Find the missing side of the right triangle.

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Example #2 Find the missing side of the right triangle.

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Example #3 Find the missing side of the right triangle.

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Example #4 Find the area of the right triangle.

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Example #5 Find the area of the right triangle.

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**Example #6 What type of triangle are each of the following?**

A. 4, 6, 7 E. 8, 8, 8 B. 15, 20, 25 F. 16, 48, 50 C. 10, 15, 20 G. 7, 8, 9 D. 13, 84, 85 H. 6, 11, 14

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**Theorem 7-8 45°-45°-90° Triangle Theorem**

In a 45°-45°-90° triangle, both legs are congruent and the length of the hypotenuse is times the length of a leg. 45° 45° 90° n n n

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**Theorem 7-9 30°-60°-90° Triangle Theorem**

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg. 30° 60° ° n n n

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Example #7 Find the remaining two sides of each figure.

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Example #8 Find the remaining two sides of each figure.

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Example #9 Find the remaining two sides of each figure.

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Example #10 Find the remaining two sides of each figure.

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Example #11 A square garden has sides 100 ft long. You want to build a brick path along a diagonal of the square. How long will the path be?

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Example #12 The distance from one corner to the opposite corner of a square playground is 96 ft. How long is each side of the playground?

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Example #13 A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden.

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Example #14 A rhombus has 10-inch sides, two of which meet to form a 30° angle. Find the area of the rhombus.

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Practice WB 7-2 # 1, 3, 5, 10, 14-19 WB 7-3 # 2, 4, 7, 10, 13, 15 EXIT

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