Download Section 4.7 ~ Isosceles and Equilateral Triangles

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Section 4.7 ~ Isosceles and Equilateral Triangles
Topics in this lesson:
• isosceles triangles
• equilateral triangles
• Base Angles Theorem
• Converse of Base Angles Theorem
Vocabulary (all on Isosceles Triangles)
legs ­ the 2 congruent sides
vertex angle
vertex angle ­ the angle formed by the legs
leg
leg
base ­ the side that is not a leg
base angles ­ the two angles that are not the vertex angle
base angle
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent.
Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent.
Corollary to the Base Angle Theorems
A triangle is equilateral if and only if it is equiangular.
base
base angle
Example 1
Complete the statement:
Example 2
Find the values of x and y in the diagram.
Example 3
State whether the given values for x, y, and z are possible or not. If not, explain.
x = 82, y = 72, z = 33
.
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