Download File - Ms. K. Owens Mathematics

Section 5.4 Isosceles and Equilateral
Triangles
EQ: What special relationships exist among the sides and angles of isosceles
and equilateral triangles?
An isosceles triangle has at least 2 congruent sides.
 The congruent sides are called the legs.
 The angle formed by the legs is called the vertex angle.
 The side opposite the vertex angle is called the base.
 The base angles are the two angles that have the base as a side.
∠____ is the vertex angle.
∠____ and ∠____ are the base angles.
Theorem
Isosceles Triangle Theorem
If two sides of a triangle are
congruent, then the angles
opposite the sides are
congruent.
Converse of the Isosceles
Triangle Theorem
If two angles of a triangle
are congruent, then the
sides opposite the angles
are congruent.
Hypothesis
Conclusion
∠____ ≅ ∠____
_____ ≅ _____
Find each angle measure.
1. 𝑚∠𝐶
2. 𝑚∠𝑆
3. 𝑚∠𝐻
4. 𝑚∠𝑁
Corollary
Equilateral Triangle
Corollary
If a triangle is equilateral,
then it is equiangular.
Equiangular Triangle
Corollary
If a triangle is equiangular,
then it is equilateral.
Hypothesis
Conclusion
∠____ ≅ ∠____
≅ ∠____
_____ ≅ _____
≅ _____
Practice using the properties of equilateral triangles:
1. Find 𝑥.
2. Find 𝑡.
3. Find 𝐽𝐿.