Transcript Isosceles and Equilateral Triangles

4.5 - Isosceles and Equilateral
Triangles
Isosceles Triangles
vertex
angle
•The congruent sides of
legs
an isosceles triangles are
called it legs.
•The third side is the
base.
•The two congruent
sides form the vertex
base
base angles
angle.
•The other two angles
are the base angles.
Theorem 4-3 Isosceles Triangle Theorem
If two sides of a triangle are congruent, then
the angles opposite those sides are congruent.
C
A  B
A
B
Given: AC  BC
Prove: A  B
(hint: draw an angle bisector for C)
Statements
C
Reasons
A
B
Theorem 4-4 Converse of the Isosceles
Triangle Theorem
If two angles of a triangle are congruent, then
the sides opposite the angles are congruent.
C
AC  BC
A
B
Theorem 4-5
The bisector of the vertex angle of an
isosceles triangle is the perpendicular bisector
of the base.
C
CD  AB and CD bisects
AB
A
D
B
A corollary is a statement that
follows immediately from a
theorem.
Corollary to Theorem 4-3
If a triangle is equilateral, then the
Y
triangle is equiangular.
X  Y  Z
X
Z
Corollary to Theorem 4-4
If a triangle is equiangular, then
the triangle is equilateral.
Y
XY  YZ  ZX
X
Z
Find the values of the variables.
Find the values of the variables.
Complete each statement.
Find the measure of each angle.
Homework
p. 213
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