Download Review for Six Weeks Test

FIRST SIX WEEKS
REVIEW
SYMBOLS &
TERMS
A
6
B
SEGMENT AB
AB  6
Endpoints A and B
A
M
B
3
3
M is the Midpoint
of AB
AM  MB
A segment has
endpoints on a number
line of -3 and 5, Find
its length.
5  (3)  8
A segment has
endpoints on a number
line of -3 and 5, find its
midpoint.
3  5 2
 1
2
2
 x1  x2 y1  y2 
,


2 
 2
 x1  x2 y1  y2 
,


2 
 2
The Midpoint of a segment
Find the midpoint of the
segment joining (3,4) and
(-5,-6).
Find the midpoint of the
segment joining (3,4) and
(-5,-6).
 x1  x2 y1  y2 
,


2 
 2
Find the midpoint of the
segment joining (3,4) and
(-5,-6).
 3  5 y1  y2 
,


2 
 2
Find the midpoint of the
segment joining (3,4) and
(-5,-6).
 3  5 y1  y2 
,


2 
 2
Find the midpoint of the
segment joining (3,4) and
(-5,-6).
 3  5 4  6 
,


2 
 2
Find the midpoint of the
segment joining (3,4) and
(-5,-6).
 3  5 4  6   2 2 
,

,

 

2   2 2
 2
 (1, 1)
a b  c
2
2
2
a b  c
2
2
2
Pythagorean Theorem–
Used to find a missing side
of a right triangle.
a b  c
2
2
2
If a=5, and b=12, then c=_?_
13
d
 x2  x1    y2  y1 
2
2
d
 x2  x1    y2  y1 
2
2
The distance formula—for finding
the length of a segment.
Find the distance between
(-2,-6) and (4, 2):
Find the distance between
(2,-6) and (-4, 2):
d
 x2  x1    y2  y1 
2
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2   y2  y1 
2
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2   y2  y1 
2
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2   2  6
2
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2    2  6 
2
 (6)  (8)
2
2
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2    2  6 
2
2
 (6)  (8)  36  64
2
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2    2  6 
2
2
 (6)  (8)  36  64
2
 100
2
Find the distance between
(2,-6) and (-4, 2):
d
 4  2    2  6 
2
2
 (6)  (8)  36  64
2
 100  10
2
ACUTE Angle
Less than 90
OBTUSE Angle
Greater
than 90 but
less than
180
RIGHT Angle
Equals 90
STRAIGHT
Angle
Equals 180
SPECIAL
PAIRS OF
ANGLES
Nonadjacent
Angles
1
2
1
2
m______
ABC  m
CBD  _______
m ABD
________
For
adjacent
angles
A
C
B
D
m______
DAB  ________
m BAC  _______
m DAC
D
B
A
C
m______
CBD  ________
m DBA  _______
m CBA
C
D
B
A
Supplementary
Angles
58
122
A
B
m A  m B  180
Vertical
Angles
1
2
Also Vertical
Angles
1
2
Linear Pair
1
2
Complementary
32
Angles
A
m A  m B  90
58
B
Congruent
A
Angles
A B
32
32
B
Angle Bisector
1
1 2
B
C
2
Conditional Statement:
Any statement that is
or can be written in ifthen form. That is,
If p then q.
Symbolically we use
the following for the
conditional statement:
“If p then q”:
pq
EXAMPLE:
If you feed the dog,
then you may go to
the movies.
EXAMPLE:
Hypothesis
If you feed the dog,
then you may go to
the movies.
EXAMPLE:
Hypothesis
If you feed the dog,
then you may go to
the movies.
Conclusion
“ALL” Statements:
When changing an “all”
statement to if-then form,
the hypothesis must be
made singular.
EXAMPLE: All rectangles
have four sides.
a figure is
BECOMES: If _______
a rectangle then _____
it has
four sides.
The Converse:
The conditional
statement formed by
interchanging the
hypothesis and
conclusion.
Symbolically, for the
conditional statement:
pq
The converse is:
q p
EXAMPLE: Form the
converse of:
If X=2 then X > 0 .
EXAMPLE: Form the
converse of:
If X=2 then X > 0 .
The Inverse:
The conditional
statement formed by
negating both the
hypothesis and
conclusion.
Symbolically, for the
conditional statement:
pq
The inverse is:
p q
EXAMPLE: Form the
Inverse of:
If X=2 then X > 0 .
EXAMPLE: Form the
Inverse of:
If X=2 then X > 0 .
The Contrapositive:
The conditional
statement formed by
interchanging and
negating the hypothesis
and conclusion.
Symbolically, for the
conditional statement:
pq
The contrapositive is:
q
p
EXAMPLE: Form the
contrapositive of:
If X=2 then X > 0 .
LOGIC:
SYLLOGISMS
Law of Syllogism
pq
qr
_________
pr
• If a figure is a rectangle, then it is
a parallelogram.
• If a figure is a parallelogram, then
its diagonals bisect each other.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• If a figure is a parallelogram, then
its diagonals bisect each other.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• If a figure is a parallelogram, then
its diagonals bisect each other.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• If a figure is a parallelogram, then
its diagonals bisect.
• __________________________
If a figure is a rectangle, then
 its diagonals bisect.
Law of Detachment
pq
p
________
q
• If a figure is a rectangle, then it is
a parallelogram.
• ABCD is a rectangle.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• ABCD is a rectangle.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• ABCD is a rectangle.
• __________________________
 ABCD is a parallelogram.
Law of Contrapositive
pq
q
________
 p
• If a figure is a rectangle, then it is
a parallelogram.
• ABCD is not a parallelogram.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• ABCD is not a parallelogram.
• __________________________

• If a figure is a rectangle, then it is
a parallelogram.
• ABCD is not a parallelogram.
• __________________________
ABCD is not a rectangle.
In the following
examples, use a law to
draw the correct
conclusion from the set
of premises.
1. If frogs fly then
toads talk.
Frogs fly.
-----------------------------

1. If frogs fly then
toads talk.
Frogs fly.
-----------------------------
 Toads talk.
2. If hens heckle then
crows don’t care.
Crows care.
-----------------------
2. If hens heckle then
crows don’t care.
Crows care.
----------------------Hens don’t heckle.
3. If ants don’t ask
then flies don’t fret.
Ants don’t ask.
----------------------------
3. If ants don’t ask
then flies don’t fret.
Ants don’t ask.
---------------------------Flies don’t fret.
PROPERTIES
IF
then
AB  BC
BC  AB
Symmetric Property
of Congruence
A A
Reflexive
Property of
Congruence
IF
AB  BC
and
BC  CD
then
AB  CD
Transitive Property
of Congruence
If
m A  m B  180
and
m B  90
then m A 90  180
Substitution
Property of
Equality
IF
AB = CD
Then
AB + BC = BC + CD
Addition Property of
Equality
If
AB + BC= CE
and CE = CD + DE
then
AB + BC = CD + DE
Transitive Property
of Equality
If
AC = BD
then
BD = AC.
Symmetric
Property of
Equality
If
AB + AB = AC
then
2AB = AC.
Distributive
Property
m Bm B
Reflexive Property
of Equality
If
2(AM)= 14
then
AM=7
Division Property of
Equality
If
AB + BC = BC + CD
then
AB = CD.
Subtraction
Property of
Equality
If
AB = 4
then
2(AB) = 8
Multiplication
Property of
Equality
Let’s see if you
remember a few
oldies but goodies...
If B is a point between
A and C, then
AB + BC = AC
The Segment
Addition Postulate
If Y is a point in the
interior of
RST
then
m RSY  m YST  m RST
Angle Addition
Postulate
IF M is the Midpoint
of AB
then
AM  MB
The Definition of
Midpoint
IF AB
bisects
then
CAD
CAB  BAD
The Definition of
an Angle Bisector
If AB = CD
then
AB  CD
The Definition of
Congruence
If
m A  90
then
A
is a right angle.
The Definition of
Right Angle
If
1
1
is a right
angle, then
the lines are
perpendicular.
The Definition of
Perpendicular
lines.
If
A B
Then
m Am B
The Definition of
Congruence
And now a few
new ones...
If
A and B
are right angles,
then
A B
Theorem: All Right
angles are congruent.
1
2
n
m
If 1 and 2 are
congruent, then lines m
and n are
perpendicular.
Theorem: If 2 lines
intersect to form
congruent adjacent
angles, then the
lines are
perpendicular.