LESSON 5 5 INEQUALITIES IN TRIANGLES OBJECTIVE To

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 Example 1: List the angles from smallest to largest Z Y X 17” Y 29” 32” Z

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. Example 2: In QRS, list the sides from smallest to largest SR QS QR Q 30° S R

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

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.

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

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

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

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