# Isosceles, Equilateral and right triangles

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```					 4.6 Isosceles,
Equilateral and
Right s
Pg 236
Standards/Objectives:
Standard 2: Students will learn and apply
geometric concepts
Objectives:
• Use properties of Isosceles and equilateral
triangles.
• Use properties of right triangles.
Assignment
•   pp. 239-240 #1-25 all
•   Chapter 4 Review – pp. 252-254 #1-17 all
•   Test after this section
•   Chapter 5 Postulates/Theorems
•   Chapter 5 Definitions
•   Binder Check
Isosceles triangle’s special
parts
A
A is the vertex angle
(opposite the base)
 B and C are base
the base)

C
B
Base
Thm 4.6
Base s thm
• If 2 sides of a  are @, the 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.
A
If seg AB @ seg
BC @ seg CA,
then A @ B @
C

B                                                         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 the hypotenuse and      A
a leg of one right  are
@ to the hypotenuse
and leg of another
right , then the s are
@.                             _

_
B         C
X              _ Y

_
If seg AC @ seg XZ
and seg BC @ seg YZ,
then  ABC @  XYZ
Z
Given: D is the midpt of seg CE,
BCD and FED are rt s and seg
BD @ seg FD.
Prove:  BCD @  FED

B                                   F

D
C                               E
Proof
Statements                 Reasons
1. D is the midpt of seg   1. Given
CE,  BCD and <FED
are rt  s and seg
BD @ to seg FD
2. Seg CD @ seg ED         2. Def of a midpt
3.  BCD @  FED           3. HL thm
Are the 2 triangles @ ?
Yes, ASA
or AAS

)                             (
Find x and y.
x   60                  y
75

90
x                   y
x
2x + 75=180          x=60     y=30
2x=105
x=52.5   y=75
Find x.
56ft

(

8xft
))
56=8x
7=x                            ((

```
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