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Isosceles and Equilateral Triangles
Isosceles Triangle Vocabulary:
Vertex Angle – The angle formed by the
congruent sides of an isosceles
triangle.
Base Angles – The two angles formed by
the base and one of the congruent sides
of an isosceles triangle.
Isosceles and Equilateral Triangles
Isosceles Triangle Theorem
• If two sides of a triangle are congruent, then
the angles opposite those sides are
congruent.
Converse of the Isosceles Triangle Theorem
• If two angles of an isosceles triangle are
congruent, then the sides opposite those
angles are congruent.
Write a two-column proof.
Given:
Prove:
.
Proof:
Statements
1.
Reasons
1. Given
2. ADB is isosceles.
2. Def. of isosceles triangles
3.
4.
3. Isosceles  Theorem
4. Given
5.
6. ABC ADC
7.
5. Def. of midpoint
6. SAS
7. CPCTC
Multiple-Choice Test Item
If
and
measure of
A. 25
Answer: A
B. 35
what is the
C. 50
D. 130
a. Name two congruent angles.
Answer:
b. Name two congruent
segments.
Answer:
Isosceles and Equilateral Triangles
Corollary 4.3
• A triangle is equilateral if and only if it is
equiangular.
Corollary 4.4
• Each angle of an equilateral triangle
measures 60 degrees.
ABC is an equilateral triangle.
a. Find x.
Answer: 30
b.
Answer: 90
bisects