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Geometry Lesson 4-7: Use Isosceles and Equilateral Triangles
Learning Target: By the end of today’s lesson we will be able to successfully use theorems about isosceles
and equilateral triangles.
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Legs: ______________________________________________________________________________
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Vertex angle: ________________________________________________________________________
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Base: ______________________________________________________________________________
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Base angles: ________________________________________________________________________
THEOREM 4.7: BASE ANGLES THEOREM
If two sides of a triangle are congruent, then the angles opposite them are congruent.
If AB  AC , then B  ________
THEOREM 4.8: CONVERSE OF BASE ANGLES THEOREM
If two angles of a triangle are congruent, then the sides opposite them are congruent.
If B  C, then AB  ________
Example 1: In FGH, FH  GH . Name two congruent angles.
COROLLARY TO THE BASE ANGLES THEOREM
If a triangle is equilateral, then it is _____________________.
COROLLARY TO THE CONVERSE OF BASE ANGLES THEOREM
If a triangle is equiangular, then it is ___________________.
***The corollaries state that a
triangle is equilateral if and
only if it is equiangular.***
Example 2: Find the measures of R, S, and T.
Example 3: Find the values of x and y in the diagram.
Example 4: The pattern at the right is present in a quilt.
a.) Explain why ADC is equilateral.
b.) Show that CBA  ADC.
Example 5:
a.) If FH  FJ , then ______  ______.
b.) If FGK is equiangular and FG = 15, then GK = ______.