Download Chapter 4 Lesson 5

Chapter 4 Lesson 5
Objective: To use and apply
properties of isosceles
triangles.
The congruent sides of an isosceles
triangle are its legs. The third side is the
base. The two congruent sides form the
vertex 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.
A  B
Theorem 4-4
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent,
then the sides opposite the angles are
congruent.
AC  BC
Theorem 4-5
The bisector of the vertex angle of an
isosceles triangle is the perpendicular
bisector of the base.
CD  AB and CD bisects AB .
Example 1: Proofs
Given: A  B
CD bisects ACB
D
Prove:
A
A
S

AC  BC
A  B
Given
ACD  BCD
Def. of  bisector
CD  CD
Reflex. Prop.
ACD  BCD AAS
AC  BC CPCTC
Example 2: Proofs
Given: AC
D
 BC
CD bisects AB
Prove: CAD  CBD
S
S
S

AC  BC
AD  BD
CD  CD
Given
Def. of segment
bisector
Reflex. Prop.
ACD  BCD SSS
CAD  CBD CPCTC
Example 3: Using Algebra
Find the values of x and y.
By Theorem 4-5, you know thatMO  LN, so
x = 90. ∆M L N is isosceles, so L  N and
mN  63.
Corollary to Theorem 4-3
If a triangle is equilateral, then the
triangle is equiangular.
X  Y  Z
Corollary to Theorem 4-4
If a triangle is equiangular, then the
triangle is equilateral.
XY  YZ  ZX
Assignment
Pg. 213
#1-2;7-16;
21-24