Warm-Up Find the group members with the same letter on their worksheet as you. Complete problems #3 & #4. Take your homework with you to be checked!

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Presentation transcript:

Warm-Up Find the group members with the same letter on their worksheet as you. Complete problems #3 & #4. Take your homework with you to be checked!

Homework Answers - Friday

Section 8.2 Notes: The Pythagorean Theorem and its Converse

Pythagorean Theorem

Example 1: Find the value of x.

Example 1: Find the value of x. b)

Pythagorean Triples 6,8,10 10,24,26 16,30,34 14,48,50 9,12,15 15,36,39 24,45,51 21,72,75 12,16,20 20,48,52 32,60,68 28,96,100

Example 2: Use a Pythagorean Triple to find the value of x. a)

Example 2: Use a Pythagorean Triple to find the value of x. b)

Example 3: a) A 20-foot ladder is placed against a building to reach a window that is 16 feet above the ground. How many feet away from the building is the bottom of the ladder?

Example 3: b) A 10-foot ladder is placed against a building. The base of the ladder is 6 feet from the building. How high does the ladder reach on the building?

In ∆𝐴𝐵𝐶 with side lengths a, b, c: (c is longest side) Converse of the Pythagorean Theorem If 𝑎 2 + 𝑏 2 = 𝑐 2 , then ∆𝐴𝐵𝐶 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒. Pythagorean Inequality Theorem 8.6 If 𝑎 2 + 𝑏 2 > 𝑐 2 , then ∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑎𝑐𝑢𝑡𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒. Pythagorean Inequality Theorem 8.7 If 𝑎 2 + 𝑏 2 < 𝑐 2 , then ∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑜𝑏𝑡𝑢𝑠𝑒 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒. You must verify that if forms ANY triangle first!

Example 4: a) Determine whether 9, 12, and 15 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Example 4: b) Determine whether 10, 11, and 13 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Pythagorean Theorem Post-It Activity

Summary! If , then ABC is _____________.

Summary! 1. Are the triangles obtuse, right, or acute? a)

Summary! 1. Are the triangles obtuse, right, or acute? b)