Download vertex angle

4-5 Isosceles and
Equilateral Triangles
Objectives
Students will be able to
Use and apply properties of isosceles and equilateral
triangles
Essential Understanding
The angles and sides of isosceles and equilateral
triangles have special relationships
Isosceles Triangles
What are some things you know about isosceles triangles?
The congruent sides are called the legs
Third side is the base
The two congruent legs form the vertex angle
The other two angles are the base angles
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 a triangle are congruent, then the sides
opposite those angles are congruent.
Example 1
Is <WVS congruent to <S? Explain
Is TR congruent to TS? Explain
Will triangle RUV is isosceles? Explain
Theorem
If a line bisects the vertex angle of an isosceles triangle,
then the line is also the perpendicular bisector of the
base.
Example
What is the value of x?
Example
Corollary to Isosceles Triangle Thm
Corollary: a theorem that can be proved easily using
anther theorem
If a triangle is equilateral, then the triangle is
equiangular
Corollary to Converse of
Isosceles Triangle Thm
If a triangle is equiangular, then the triangle is
equilateral
Example
If I have and equilateral triangle, what are the measures
of the angles of that triangle?
Homework
Pg. 254 – 256
6 – 12 even, 16 – 20, 22, 25, 28, 30, 32
14 problems