Warm Up Use the figure for problems 1 and 2. round to the nearest hundredth 1) Find the height a of the triangle c 10 8 a 6 9 2) Find the length of side.

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Presentation transcript:

Warm Up Use the figure for problems 1 and 2. round to the nearest hundredth 1) Find the height a of the triangle c 10 8 a 6 9 2) Find the length of side c c = 82 + 92 c = 64 + 81 c = 145

Warm Up 5 units 6 units ??? B Find the distances between the points C and D E and F A and B C 5 units A 6 units ??? F E D

The Pythagorean Thm and its Converse Lesson 3-9 The Pythagorean Thm and its Converse You'll Learn how to Use the Distance formula and the converse of PYTH.THM

They form a right triangle They DO NOT form a right triangle Use the converse of Pythagorean Theorem The converse of the Pythagorean Theorem If any positive numbers, a, b, and c satisfy the Pythagorean theorem a2 + b2 = c2 then a, b and c form a right triangle EXAMPLE 1 Tell whether the given sides lengths form a right triangle. i) 8, 15, 17 ii) 8, 10, 13 Checking (c is the longest side) Checking (c is the longest side) a2 + b2 = c2 a2 + b2 = c2 82 + 152 = 172 82 + 102 = 132 64 + 225 = 289 64 + 100 = 169 289 = 289 164 = 169 They form a right triangle They DO NOT form a right triangle

Find the distance between the points. Use the Distance Formula EXAMPLE 1 Find the distance between the points. Method1: Using Pythagorean Theorem B 5 c = 32 + 52 (4, 4) x2, y2 3 c c = 9 + 25 A (-1, 1) c = 34 x1, y1 Method2: Using Distance Formula 4 -1 4 1 5 3 25 9 34

Find the distance between the points EXAMPLE 2 Find the distance between the points Using Distance Formula -4 -3 4 -3 (-4, 0) x1, y1 16 9 25 (0, -3) x2, y2

Lesson Quiz: Part I Find the length of the diagonal of the rectangle. 1. width = 9 in., length = 40 in. 2. base length = 20 m, height = 15 m.

Lesson Quiz: Part II Find the distance between the points to the nearest tenth. 3. Q and R 4. S and T

Lesson Quiz: Part III Tell whether the given side lengths form a right triangle. 5. 12 cm, 13 cm, 16 cm no 6. 11 ft, 60 ft, 61 ft yes

Lesson Quiz for Student Response Systems 1. Find the length of the diagonal of the rectangle. width = 5 m, length = 12 m A. 8 m B. 11 m C. 13 m D. 17 m 10 10

Lesson Quiz for Student Response Systems 2. Find the distance between the points to the nearest tenth. Q and S A. 6.0 m B. 6.1 m C. 7.0 m D. 37.1 m 11 11

Lesson Quiz for Student Response Systems 3. Tell whether the given side lengths form a right triangle. 12 ft, 13 ft, 14 ft A. yes B. no 12 12