Inequalities in Triangles Inequalities in Triangles Triangles have

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Inequalities in Triangles

Inequalities in Triangles • Triangles have two important properties: – Property #1: • The smallest angle is across from the smallest side (S for Smallest) • The medium angle is across from the medium side (M for Medium) • The largest angle is across from the largest side (L for Largest)

Visuals L⁰ Min Sin 95⁰ 7 in S⁰ M⁰ Lin 9 in 40⁰ 45⁰ 12 in **There is no formula to find the side lengths actual measures – you just compare them!

Examples • List the sides of the triangle shown in order from least to greatest. c, a, b

More Examples JK, JL, KL XY, YZ, XZ <B, <C, <A QR, PR=PQ

Property #2: The two smallest sides of a triangle must add up to be larger than the largest.

Examples • Can the following side measures be made to form a triangle? a. 6, 9, 13 yes b. 4, 8, 12 no c. 15, 8, 31 no d. 6, 14, 15 yes e. 10, 8 yes f. 4, 2, 5 yes

Examples To describe the possible lengths of the third side of a triangle given the length of the other two sides: You must write an inequality. There are several solutions! Example: 6 in. , 9 in, 3 15 _____< x < _____ (subtract) (add)

More Examples 20. 4 ft, 12 ft 8 < x < 16 21. 9 m, 18 m 9 < x < 27 22. 21 yd, 16 yd 5 < x < 37 23. 22 in, 2 ft 2 in < x < 46 in 24. 24 in, 1 yd 12 in < x < 60 in

More Examples Is it possible to build a triangle using the given side lengths? If so, order the angle measures of the triangle from least to greatest. Yes: <S, <R, <T Yes: <B, <C, <A

Examples Describe the possible values of x. 2 < 2 x -2 < 12 4 < 2 x < 14 2<x<7 10 < 4 x + 2 < 26 8 < 4 x < 24 2<x<6