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Section 4.5- Isosceles and Equilateral Triangles Essential Question: What special relationships exist in isosceles and equilateral triangles? Do Now: Fill in the blank with either: one, two, or three. An equilateral triangle has ____________ congruent sides. An isosceles triangle has ________ congruent sides. Parts of an Isosceles Triangle Example 1: Using the Isosceles Triangle Theorems ̅̅̅? Explain. ̅̅̅̅ congruent to ̅𝑇𝑆 a. Is ∠WVS congruent to ∠S? Is 𝑇𝑅 b. Can you conclude that ΔRUV is isosceles? Explain. Example 2: Using Algebra and Perpendicular Bisectors in Isosceles Triangles Suppose the m ∠A=27. What is the value of x? Relationships in Equilateral Triangles If _____________________, then _____________________. If _____________________, then _____________________. Example 3: Finding Angle Measures Suppose the triangles are isosceles triangles, where ∠ADE, ∠DEC, and ∠ECB are vertex angles. If the vertex angles each have a measure of 58°, what are m ∠A and m ∠BCD? Group Work: 1. An exterior angle of an isosceles triangle has a measure of 100°. Find two possible sets of measures for the angles of the triangle. (Draw a diagram to help you.) 2. 3. (3 steps) Statements HW: p. 254-256 #6-12 evens, 13-20, 30-32 Reasons