Presentation on theme: "Triangle Inequalities"— Presentation transcript:
1Triangle Inequalities Objective:Discover the inequalities between sides and angles of a triangle
21. Draw 3 segments on your paper CA = 3 cm AT = 4 cmCT = 8 cm3. Draw 3 more segments on your paper DO = 3 cmDG = 4 cmOG = 7 cm2. Construct or draw ∆CAT4. Construct or draw ∆DOGThe sum of the lengths of any two sides of a triangle is _________ than the third side.Triangle Inequality Conjecturegreater
31. Draw a scalene triangle use a straightedge MsLMeasure all angles and label:L = largest angleM = middle angleS = Smallest anglel3. Measure all sides and label:ml = largest sidem = middle sides = smallest sideS4. Any patterns?In a triangle, if one side is longer than another, then the angle opposite the longer side is _______________________________________Side-Angle Inequality Conjecturelarger than the angle opposite the shorter side.
4Triangle Exterior Angle Conjecture 1. Draw a scalene triangle use a straightedge2. Extend one side beyond triangleExterior angle: an angle that forms a linear pair with an interior angleRemote interior angles: two angles that do not share a vertex with an exterior angle3. Measure exterior and remote interior angles.Triangle Exterior Angle ConjectureThe measure of an exterior angle of a triangle ______________________________________________.is equal to the sum of the remote interior angles
5Examples Pg 216 #1-17, 19-22 List a, b, c from smallest to greatest. Triangle or not?8cm , 10 cm, 12 cm4cm, 4cm, 8cmC, B, AYesAPg 216 #1-17, 19-22NoB550Find x800720C1200x400