Download Honors Geometry Section 4.4 Isosceles Triangle Theorem

Honors Geometry Section 4.4
Isosceles Triangle Theorem
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) Def. of CAs
E & CDB are CAs
4) A  CBD; E  CDB 4) CAP
) A  E
) CA  CE
) CAE is isosceles
5) Substitution 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
6) AIAT
) 1  2
7) Subst. Prop
) MT bisects SMR
) Def. of Bisects