Isosceles and Equilateral Triangles
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Transcript Isosceles and Equilateral Triangles
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