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October 05, 2011 Objective: To apply theorems and corollaries to solve problems and write proofs about isosceles triangles. What is the definition of an isosceles triangle? October 05, 2011 Do you notice anything else? October 05, 2011 What do you know about an isosceles triangle now? Isosceles Triangle Theorem · If two sides of a triangle are congruent, then the angles opposite those sides are _______________. BAIT (Base Angles Isosceles Triangle) · If two base angles are congruent, then the sides opposite those angles are __________. October 05, 2011 Vertex Angle Bisector (VAB) Cor. · The bisector of the vertex angle of an isosceles triangle is _________________________________. October 05, 2011 Corollaries · An equilateral triangle is equiangular. · An equilateral triangle has three 60 degree angles. · An equiangular triangle is equilateral. October 05, 2011 1. Write and test a conjecture about the lengths of the sides of a triangle. 2. Write and test a conjecture about the relationship of a triangle's side lengths and angle measures. Materials you can use: · Compass 3 in, 4 in, 5 in 4 cm, 5 cm, 9 cm Triangle Inequality Theorem · The sum of the lengths of any two sides of a triangle is ____________________________ . Theorem · In a triangle, the smallest angle is opposite the ____________________ and the largest angle is opposite the ___________________ . October 05, 2011 The lengths of two sides of a triangle are 8 and 13. Then, the length of the third side must be greater than ______ but less than _________ . Is is possible for a triangle to have sides with lengths indicated? a) 6, 8, 10 b) 3, 4, 8 c) 2.4, 4.1, 5