Inequalities in Triangles

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Triangle Inequalities

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Presentation transcript:

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

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 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? 6, 9, 13 4, 8, 12 15, 8, 31 6, 14, 15 10, 10, 8 4, 2, 5 yes no no yes yes 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, _________< x < __________ (subtract) (add) 3 15

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