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ESSENTIAL QUESTION: What kind of triangle is there when c 2 is not equal to a 2 + b 2

Understand triangle types when c^2 is not equal to a^2 + b^2 through examples demonstrating acute, right, and obtuse triangles using the Pythagorean Theorem. Practice identifying triangle classifications based on side lengths.

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ESSENTIAL QUESTION: What kind of triangle is there when c 2 is not equal to a 2 + b 2

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  1. ESSENTIAL QUESTION: What kind of triangle is there when c2 is not equal to a2+ b2

  2. The Converse of the Pythagorean Theorem • If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

  3. Example 1 ? ? ? = = = = = = c2a2 + b2 Compare c2 with a2 + b2. 202122 + 162 Substitute 20 for c, 12 for a, and 16 for b. 400 144 + 256 Multiply. 400 = 400 Simplify. Verify a Right Triangle Is ∆ABC a right triangle? SOLUTION It is true that c2 = a2 + b2. So, ∆ABC is a right triangle. ANSWER

  4. Right Triangle???? • c2 = a2 + b2 RIGHT • c2 > a2 + b2 OBTUSE • c2 < a2 + b2 ACUTE

  5. Example 2 c2a2 + b2 Compare c2 with a2 + b2. ? ? ? = = = = = = 242 + 52 Substitute for c, 4 for a, and 5 for b. 35 35 Multiply. 35 16 + 25 I DO…. Show that the triangle is an acute triangle. SOLUTION Compare the side lengths. 35 < 41 Simplify. Because c2 < a2 + b2, the triangle is acute. ANSWER

  6. Example 3 c2a2 + b2 ? ? = = = = 225 64 + 144 Multiply. I DO…. Show that the triangle is an obtuse triangle. SOLUTION Compare the side lengths. 225 > 208 Simplify. Becausec2 > a2 + b2, the triangle is obtuse. ANSWER

  7. Example 4 c2a2 + b2 ? ? ? = = = = = = 8252 + 62 64 25 + 36 Multiply. WE DO…. Classify the triangle as acute, right, or obtuse. SOLUTION 64 > 61 Simplify. Becausec2 > a2 + b2, the triangle is obtuse. ANSWER

  8. Example 5 SOLUTION a. b. c2a2 + b2 c2a2 + b2 ? ? ? ? ? ? = = = = = = = = = = = = 7242 + 62 372122 + 352 49 16 + 36 1369 144 + 1225 WE DO.… Classify the triangle with the given side lengths as acute, right,or obtuse. a. 4, 6, 7 b. 12, 35, 37 49 < 52 1369 = 1369 The triangle is acute. The triangle is right.

  9. Checkpoint Classify the triangle as acute, right, or obtuse. Explain. YOU DO…. 1. 2. 3.

  10. Checkpoint Classify the triangle as acute, right, or obtuse. Explain. Classify Triangles 1. obtuse; 62 > 22 + 52 ANSWER 2. right; 172 = 82 + 152 ANSWER 3. acute; 72 < 72 + 72 ANSWER

  11. Checkpoint Use the side lengths to classify the triangle as acute, right, or obtuse. Classify Triangles 7, 24, 24 4. 5. 7, 24, 25 6. 7, 24, 26

  12. Checkpoint Use the side lengths to classify the triangle as acute, right, or obtuse. Classify Triangles 4. 7, 24, 24 acute ANSWER 5. 7, 24, 25 right ANSWER 6. 7, 24, 26 obtuse ANSWER

  13. Hw Practice 4.5B

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