Triangle Inequalities

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Presentation transcript:

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

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

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

Triangle Exterior Angle Conjecture 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. Triangle Exterior Angle Conjecture The measure of an exterior angle of a triangle ______________________________________________. is equal to the sum of the remote interior angles

Examples Pg 216 #1-17, 19-22 List a, b, c from smallest to greatest. Triangle or not? 8cm , 10 cm, 12 cm 4cm, 4cm, 8cm C, B, A Yes A Pg 216 #1-17, 19-22 No B 550 Find x 800 720 C 1200 x 400