Warmup
Which is the correct definition of isosceles?
a.) a triangle with at least 2 congruent sides
b.) a triangle with exactly 2 congruent sides
4.5 Isosceles Triangles
LEQ: How can we use properties
of isosceles triangles to construct
proofs?
Word Bank
Leg
Leg
Vertex
Base
Base Angles
Given
Proof:
ABC is isosceles. Prove m<A=m<B.
Statements
1.) AC=BC
C
Reasons
1.) Definition of Isosceles
*Construct CD so that it bisects <C*
2.)m<ACD=m<BCD
2.)Defn. of bisect
3.) CD=CD
3.) reflexive property
4.) ACD BCD
4.) SAS
What can you conclude about <A and <B?
5.) <A <B
5.) CPCTC
A
D
B
Isosceles Triangle Theorem:
If 2 sides of a triangle are congruent, then the
base angles are congruent as well.
Converse:
If the base angles of a triangle are congruent,
then the 2 opposite legs of the triangle are
congruent as well.
What kind of statement is this?
Given BC=AC, answer the following:
a.) If m<1=140, m<2=_____,
C
m<3=______ and m<4=______
1
2
b.) If m<4=65, m<2=_____,
m<3=______and
m<1=______.
A
3
4
B
Corollaries (small theorem that
follow a big theorem)
• An equilateral triangle is also equiangular.
• An equiangular triangle has all 60 angles.
Perpendicular bisector:
• Draw an isosceles triangle
• Bisect the vertex
• What do you notice about the
intersection of the bisector and
the base?
Corollary 3
The bisector of the vertex of an isosceles
triangle is a perpendicular bisector of the
base.
(divides the base in half and is perpendicular to
the base)
Try examples 1-3.
Ex. 1
An exterior angle of an isosceles triangle has
the measure 11o degrees. What are the 2
possible sets of measures for the angles of
the triangle?40,70,70 and 70,55,55
110
40
110
70
70+x+x=180
x=55
x
x
70
70 110
Ex. 2: Find the values of m and n:
m+n=
45
60
m=
n
m