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LESSON 5-5 INEQUALITIES IN TRIANGLES

LESSON 5-5 INEQUALITIES IN TRIANGLES. OBJECTIVE: To use inequalities involving angles and sides of triangles. Theorem 5-10. If a triangle is scalene, then the largest angle. lies opposite the longest side. and the smallest angle. lies opposite the shortest side. X.

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LESSON 5-5 INEQUALITIES IN TRIANGLES

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  1. LESSON 5-5 INEQUALITIES IN TRIANGLES OBJECTIVE: To use inequalities involving angles and sides of triangles

  2. Theorem 5-10 If a triangle is scalene, then the largest angle lies opposite the longest side and the smallest angle lies opposite the shortest side. X Example 1: List the angles from smallest to largest 17” 29” Y Z Y X Z 32”

  3. SR QS QR Theorem 5-11(Converse of Theorem 5-10) If a triangle is scalene, then the longest side lies opposite the largest angle, and the shortest side lies opposite the smallest angle. Q Example 2: In QRS, list the sides from smallest to largest 30° S R

  4. Therefore VT is shortest Example 3: In TUV, which side is the shortest? Use  sum to find mT. mT = 60°, so U is smallest T V 58° 62° U

  5. Theorem 5-12 The Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  6. Example 4: Can a triangle have sides with the given lengths? Explain. b) 3cm., 6cm., 10cm. a) 3ft., 7ft., 8ft. Yes, 3 + 7 > 8 NO, 3 + 6 < 10

  7. Example 5: A triangle has sides of lengths 8cm and 10cm. Describe the lengths possible for the third side. Let x = the length of the 3rd side. The sum of any 2 sides must be greater than the 3rd.

  8. So, there are 3 possibilities. x + 8 > 10 x > 2 8 + 10 > x 18 > x x < 18 x + 10 > 8 x > -2 So, x must be longer than 2cm & shorter than 18cm. 2 < x < 18

  9. ASSIGNMENT: Page 277 #4-25, 34-36, 43-46

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