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