Lesson 5 4

Lesson 5-4 Triangle Inequalities

Triangle Inequality ,[object Object],[object Object],54  37  89  B C A

Triangle Inequality – examples… ,[object Object],C A B

Triangle Inequality – examples … ,[object Object],(7x + 8) ° + (7x + 6 ) ° + (8x – 10 ) ° = 180° 22 x + 4 = 180 ° 22x = 176 X = 8 m<C = 7x + 8 = 64 ° m<A = 7x + 6 = 62 ° m<B = 8x – 10 = 54 ° 8x-10 7x+6 7x+8 C A B

Converse Theorem & Corollaries ,[object Object],[object Object],[object Object]

Triangle Inequality Theorem: ,[object Object],[object Object],[object Object],[object Object],Example: Determine if it is possible to draw a triangle with side measures 12, 11, and 17. 12 + 11 > 17  Yes 11 + 17 > 12  Yes 12 + 17 > 11  Yes

Finding the range of the third side : ,[object Object],[object Object],Example: Given a triangle with sides of length 3 and 8, find the ranges and possible values of the third side. The maximum value (if x is the largest side of the triangle) 3 + 8 < x 11 < x The minimum value (if x is not that largest side of the ∆) 8 – 3 > x 5> x Range of the third side is 5 < x < 11 .

Lesson 5 4

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