Honors Geometry Section 4.4
Isosceles Triangle Theorem
Goals for today:
1. Identify the parts of an isosceles triangle.
2. Learn and apply the Isosceles Triangle
Theorem and its converse.
3. Learn how we use the definition of an
isosceles triangle, the ITT and its converse in
proofs.
Recall that an isosceles is a triangle with
two congruent sides
_________________.
The congruent sides are called the ____
legs
and the noncongruent side is called
base The angle formed by the two
the_____.
vertex angle while the
legs is called the ___________
two angles at each end of the base are
called ___________.
base angles
Theorem 4.4.1
Isosceles Triangle Theorem (ITT)
If two sides of a triangle are
congruent, then the angles
opposite those sides are
congruent.
A  C
Theorem 4.4.2 Converse of the
Isosceles Triangle Theorem (ITTC)
If two angles of a triangle are
congruent, then the sides opposite
those angles are congruent.
Examples: Solve for x.
2 x  11  64  64  180
2 x  117  180
2 x  63
x  31 . 5
180  38  142
142 / 2  71
180  71  109
180 / 3  60
6 x  11  8 x  12
23  2 x
x  11 . 5
3 x  6  5 x  15
21  2 x
x  10 . 5
1) CB  CD , BD // AE
1) Given
2)  CBD   CDB
2) ITT
3)  A &  CBD are CAs
3) D ef. of CAs
 E &  CDB are CAs
4)  A   CBD;  E   CDB
) A  E
) CA  CE
)  CAE is isosceles
4) CAP
5) Substituti on Prop.
) ITTC
) Def.
of Isosceles
1) MA  MR , MT // AR
1) Given
2)  A   R
2 ) ITT
3 )  A &  1 are CAs
3 ) Def. of CAs
4 )  A  1
4 ) CAP
5 )  R &  2 are AIAs
5 ) Def. of AIAs
6)  R   2
) 1   2
) MT bisects  SMR
6 ) AIAT
7 ) Subst. Prop
) Def. of Bisects