4'6 Isosceles, Equilateral and Right s

1
4.6 Isosceles, Equilateral and Right ?s

• Pg 236

2
Standards/Objectives

• Standard 2 Students will learn and apply
  geometric concepts
• Objectives
• Use properties of Isosceles and equilateral
  triangles.
• Use properties of right triangles.

3
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

4
Isosceles triangles special parts
A

• ?A is the vertex angle (opposite the base)
• ? B and ?C are base angles (adjacent to the base)

Leg
Leg
C
B
Base
5
Thm 4.6Base ?s thm

• If 2 sides of a ? are _at_, the the ?s opposite them
  are _at_.( the base ?s of an isosceles ? are ?)

A
If seg AB _at_ seg AC, then ? B _at_ ? C
)
(
B
C
6
Thm 4.7Converse of Base ?s thm

• If 2 ?s of a ? are _at_, the sides opposite them are
  _at_.

A
If ? B _at_ ? C, then seg AB _at_ seg AC
)
(
C
B
7
Corollary to the base ?s thm

• If a triangle is equilateral, then it is
  equiangular.

A
If seg AB _at_ seg BC _at_ seg CA, then ?A _at_ ?B _at_ ?C
B
C
8
Corollary to converse of the base angles thm

• If a triangle is equiangular, then it is also
  equilateral.

A
)
If ?A _at_ ?B _at_ ?C, then seg AB _at_ seg BC _at_ seg CA
)
B
(
C
9
Example find x and y

• X60
• Y30

Y
X
120
10
Thm 4.8Hypotenuse-Leg (HL) _at_ thm
A

• If the hypotenuse and a leg of one right ? are _at_
  to the hypotenuse and leg of another right ?,
  then the ?s are _at_.

_
B
C
_
Y
_
X
_
If seg AC _at_ seg XZ and seg BC _at_ seg YZ, then ?
ABC _at_ ? XYZ
Z
11
Given D is the midpt of seg CE, ?BCD and ?FED
are rt ?s and seg BD _at_ seg FD.Prove ? BCD _at_ ?
FED
B
F
D
C
E
12
Proof

• Statements
• D is the midpt of seg CE, ? BCD and ltFED are rt ?
  s and seg BD _at_ to seg FD
• Seg CD _at_ seg ED
• ? BCD ? ? FED

• Reasons
• Given
• Def of a midpt
• HL thm

13
Are the 2 triangles _at_ ?
(
Yes, ASA or AAS
)
)
(
(
(
14
Find x and y.
y
x
60
75
90
y
x
x
x60
2x 75180 2x105 x52.5
y30
y75
15
Find x.
)
56ft
(
8xft
)
))
568x 7x
((