Download Isosceles, Equilateral and right triangles

4.6 Isosceles, Equilateral and
Right s
Isosceles triangle’s special parts
A is the vertex
A
angle (opposite the
base)
 B and C are
base angles
(adjacent to the
base)
B
C
Base
Thm 4.6
Base s thm
• If 2 sides of a  are @, then the s opposite them
are @.( the base s of an isosceles  are @)
A
If seg AB @ seg AC,
then  B @  C
B
C
Thm 4.7
Converse of Base s thm
• If 2 s of a  are @, the sides opposite them are @.
A
If  B @  C,
then seg AB @
seg AC
B
C
Corollary to the base s thm
• If a triangle is equilateral, then it is equiangular.
If seg AB @ seg
BC @ seg CA,
then A @ B @
C
B
A
C
Corollary to converse of the base
angles thm
)
• If a triangle is equiangular, then it is also
equilateral.
A
If A @ B @ C, then seg AB @ seg BC @
seg CA
B
(
C
Example:
find x and y
• X=60
• Y=30
X
120
Y
Thm 4.8
Hypotenuse-Leg (HL) @ thm
If seg AC @ seg XZ
and seg BC @ seg YZ,
then  ABC @  XYZ
_
B
C
_ Y
_
X
A
_
• If the hypotenuse and
a leg of one right 
are @ to the
hypotenuse and leg of
another right , then
the s are @.
Z
Given: D is the midpt of seg CE,
BCD and FED are rt s and
seg BD @ seg FD.
Prove:  BCD @  FED
B
C
F
D
E
Proof
Statements
1. D is the midpt of seg
CE,  BCD and
<FED are rt  s and
seg BD @ to seg FD
2. Seg CD @ seg ED
3.  BCD @  FED
Reasons
1. Given
2. Def of a midpt
3. HL thm
Are the 2 triangles @ ?
Yes, ASA
or AAS
)
(
Find x and y.
x
75
y
60
90
y
x
2x + 75=180
2x=105
x=52.5
y=75
x
x=60
y=30
Find x.
56ft
(
8xft
))
56=8x
7=x
((