1 / 11

7.2 Converse of Pythagorean Theorem

7.2 Converse of Pythagorean Theorem. REMEMBER:. The hypotenuse of a triangle is the longest side. Theorems:. Theorem 7.2: Converse of the Pythagorean Theorem:

jerome
Download Presentation

7.2 Converse of Pythagorean Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 7.2 Converse of Pythagorean Theorem

  2. REMEMBER: • The hypotenuse of a triangle is the longest side.

  3. Theorems: Theorem 7.2: 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 2 sides, then the triangle is a RIGHT triangle. In General: If c2 = a2 + b2 then is a RIGHT triangle.

  4. Theorems: Theorem 7.3: If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other 2 sides, then the triangle is an ACUTE triangle. In General: If c2 < a2 + b2 then is an ACUTE triangle.

  5. Theorems: Theorem 7.4: If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other 2 sides, then the triangle is an OBTUSE triangle. In General: If c2 > a2 + b2 then is an OBTUSE triangle.

  6. Example 1 • Tell whether the triangle is a right triangle. . = 17.44 c = = 142 + 102 a = = b 304 = 196 + 100 304 = 296 Not a right triangle

  7. Example 2 a b c = 72 + 142 = 15.65 245 = 49 + 196 245 = 245 Yes, a right triangle Tell whether the the given side lengths of a triangle can represent a right triangle

  8. Example 3 a • Decide if the segment lengths form a triangle. If so, would the triangle be acute, obtuse, or right? • Must use Triangle Inequality Theorem to check the segments can make a triangle. = 39.34 c2 ? a2 +b2 Step 2: Step 1: ? 242 + 302 24 + 30 = 54 So 54 > 39.34 1548 ? 576 + 900 1548 ? 1476 so: 30 + 39.34 = 69.34 So 69.34 > 24 1548 > 1476 so: 24 + 39.34 = 63.34 So 63.34 > 30 The triangle is OBTUSE Is a triangle!

  9. Example 3 b c2 ? a2 +b2 Step 2: Step 1: 122 ? 82 + 102 8 + 10 = 18 So 18 > 12 144 ? 64 + 100 144 ? 164 so: 10 + 12 = 22 So 22 > 8 144 < 164 so: 8 + 12 = 20 So 20 > 10 The triangle is ACUTE Is a triangle! Decide if the segment lengths form a triangle. If so, would the triangle be acute, obtuse, or right? Must use Triangle Inequality Theorem to check the segments can make a triangle.

  10. Example 4 In order to be directly north, there must be a RIGHT angle! a = 305 ft b = 749 ft c = 800 ft 8002 = 3052 + 7492 640,000= 654,026 No, not directly north because it does not form a right triangle.

  11. Assignment Section 7.2 Pg 444; 1, 3-14, 16-21, 25-26, 29, 35, 36, 43

More Related