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Triangle Inequalities Objective: Discover the inequalities between sides and angles of a triangle

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The sum of the lengths of any two sides of a triangle is _________ than the third side. 1. Draw 3 segments on your paper CA = 3 cm AT = 4 cm CT = 8 cm 2. Construct or draw CAT Triangle Inequality Conjecture greater 3. Draw 3 more segments on your paper DO = 3 cm DG = 4 cm OG = 7 cm 4. Construct or draw DOG

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In a triangle, if one side is longer than another, then the angle opposite the longer side is _________________ ______________________ Side-Angle Inequality Conjecture 1. Draw a scalene triangle use a straightedge 2.Measure all angles and label: 3. Measure all sides and label: 4. Any patterns? larger than the angle opposite the shorter side. L M S l s m L = largest angle M = middle angle S = Smallest angle l = largest side m = middle side s = smallest side

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The measure of an exterior angle of a triangle ______________________________________________. 1. Draw a scalene triangle use a straightedge 2. Extend one side beyond triangle Exterior angle: an angle that forms a linear pair with an interior angle Remote interior angles: two angles that do not share a vertex with an exterior angle 3. Measure exterior and remote interior angles. is equal to the sum of the remote interior angles Triangle Exterior Angle Conjecture

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x Examples Triangle or not? 8cm, 10 cm, 12 cm 4cm, 4cm, 8cm B A C List a, b, c from smallest to greatest. Yes No C, B, A Find x Pg 216 #1-17, 19-22

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