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SB En Geom 45 Completed.notebook October 03, 2012 Lesson 45 Isosceles and Equilateral Triangles Isosceles triangles triangle with at least two sides congruent legs the two congruent sides base the noncongruent side Vertex Angle vertex angle angle formed by the legs base angles angles opposite the legs Leg Leg Base Angle Base Angle Base Oct 78:28 AM Thm 43 Isosceles Triangle Thm If two sides of a triangle are congruent, then the angles opposite those sides are congruent. then If Thm 44 Converse of Isosceles Triangle Thm If two angles of a triangle are congruent, then the sides opposite the angles are congruent. If then Thm 45 The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Oct 78:32 AM 1 SB En Geom 45 Completed.notebook October 03, 2012 X Prove the Isosceles Triangle Thm. 12 Given: XY ≅ XZ, XB bisects <YXZ Prove: <Y ≅ <Z Y Z B 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. Oct 78:38 AM Expl 1. Explain why each statement is true. T a. <WVS ≅ <S U b. TR ≅ TS W R V S Ckpt 1. Can you deduce that ΔRUV is isosceles? Explain. Oct 78:41 AM 2 SB En Geom 45 Completed.notebook October 03, 2012 Expl 3. Find the value y. M y a. 17 b. 27 c. 54 d. 90 N 63 O L Ckpt 2. Suppose m<L = 43. Find the values of y. Oct 78:45 AM corollary a statement that follows immediately from a theorem Corollary to Thm. 43 If a triangle is equilateral, then it is equiangular. If, then Corollary to Thm 44 If a triangle is equiangular, then it is equilateral. If, then Oct 78:49 AM 3 SB En Geom 45 Completed.notebook October 03, 2012 Expl 3. Find x. X Ckpt 3. What is the measure of the angle at each outside corner of the path? Oct 78:53 AM Homework Lesson 4-5 1-32 Oct 78:57 AM 4