Download Review Program

Go To The
Head of the
Class-Review
Game
Rules: A question
starts with a player.
If that player answers
correctly he/she
keeps his/her seat.
If the player
misses, then the
question goes to
the next player. If
missed, it goes to
the next player...
…and continues until
someone gets it
correct. That
student moves to the
seat where the
question started...
…and everyone who
missed the question
moves back one seat.
The object of the
game is to occupy
and keep the #1
seat.
Questions with a limited
number of possible
responses will not be
offered indefinitely. A
substitute question will
be posed.
It is important to
listen to previous
responses. They will
not be repeated for
you.
The first person to
receive a question
will have a
maximum of 30
seconds to answer.
Every person after
that has only 10
seconds to reply.
Be ready when
called upon.
If the question is on a
yellow screen, expect to
solve a problem.
Have calculator, paper
& pencil ready.
If the background is
orange, name the
definition, property,
theorem, etc, that
supports the given
conclusion.
If the question is on
a green screen, it
requires just a short
answer.
Time to Play:
READY?
(begin)
1
2
Then m 1 m 2  180
The Supplement
Theorem
(The angles in a linear
pair are supplementary.)
1
2
Then
1
2
The Vertical Angles
Theorem:
Vertical Angles are
congruent.
If
A and B
are right angles,
then
A B
The Right Angle
Theorem:
All Right
angles are congruent.
Two angles are
complementary. One
is 32 degrees. What
is the measure of the
other one?
ANSWER:
58 degrees
What do we call 2
non-adjacent angles
that are formed when
2 lines intersect?
Answer:
Vertical Angles
Two angles are
supplementary. One
angle is 73 degrees,
find the measure of
the other one.
Answer:
107 degrees
What do we call 2
lines that intersect
to form right
angles?
Answer:
Perpendicular Lines
Complete this theorem:
If 2 angles are
complementary to the
same angle…...
Answer:
… then they are
congruent to each
other.
Remember the
“Key” to setting up
equations in
Geometry...
You usually do one
of 2 things…
- Set two
expressions equal
to each other
Or….
-Add expressions
together and set
their sum equal to
something else.
8x+25
Find x
4x -1
Answer:
8x+25 + 4x - 1 = 180
12x+24=180
12x=156
x=13
7x-10
Find x
5x+12
Answer:
7x-10 = 5x + 12
2x-10 = 12
2x = 22
x = 11
According to the
Supplement
Theorem, what kind
of angles are
supplementary?
Answer:
The angles in a
Linear Pair
Complete this Theorem:
If 2 lines intersect to
form congruent
adjacent angles,
then….
…then the lines are
perpendicular.
Angle A is 30 degrees.
Angle B is complementary
to Angle A. Angle C is
complementary to Angle B.
Find the measure of
Angle C.
Answer: Angle C is
30 degrees.
Angle A is 40 degrees.
Angle B is complementary
to Angle A. Angle C is
supplementary to Angle B.
Find the measure of
Angle C.
Answer: Angle C is
130 degrees.
A= 40 => B= 50
If
A and B are
supplementary,
then
m A  m B  180
The Definition of
Supplementary
Angles
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 and B are
complementary, and A
and C are
complementary, then
B C
Congruent
Complements
Theorem: If 2 angles
are complementary to
the same angle, they
are congruent to each
other.
If
A and B are
complementary,
then
m A  m B  90
The Definition
of
Complementary
Angles
The
Supplement
Theorem:
The angles in a
Linear
Pair
_____ ____ are
supplementary.
x
y
Vertical
_______
angles
are congruent.
COMPLETE: When 2 parallel
lines are cut by a transversal...
•
•
•
•
Corresponding Angles are congruent
Alternate Interior Angles are congruent
Alternate Exterior Angles are congruent
Consecutive Interior Angles are
supplementary
COMPLETE: When 2 lines are
cut by a transversal so that...
•
•
•
•
Corresponding Angles are congruent
Alternate Interior Angles are congruent
Alternate Exterior Angles are congruent
Consecutive Interior Angles are
supplementary
…Then the lines are parallel.
+
= 180
According to
their definition,
Perpendicular
lines
____________
intersect to
form right
angles.
What term describes the
two lines?
Parallel
What term describes the
two lines?
Skew
Identify the type
of angles pictured
Corresponding Angles
Alternate Exterior Angles
Consecutive Interior Angles
Alternate Interior Angles
Vertical Angles
Corresponding Angles
A Linear Pair
p
r
s
1 2
3 4
5 6
7 8
If p  r , and p  s then r // s.
The Perpendicular Transversal Converse
Theorem
1 2
3 4
r
s
5 6
7 8
If
3
6 then r // s
Alternate Interior Angles Converse
Theorem
p
r
s
1 2
3 4
5 6
7 8
If r // s then m 4  m 6  180
Consecutive Interior Angles
Theorem
p
1 2
3 4
r
s
5 6
7 8
If r // s then m 4  m 8
Corresponding Angles Postulate
p
r
s
1 2
3 4
5 6
7 8
m 7  m 8  180
The Supplement Theorem
1 2
3 4
r
s
5 6
7 8
If
2
7 then r // s
Alternate Exterior Angles Converse
Theorem
p
1 2
3 4
r
s
5 6
7 8
5
8
Vertical Angles Theorem
p
r
s
1 2
3 4
5 6
7 8
If m 3  5  180 then r // s
Consecutive Interior Angles Converse
Theorem
p
r
s
1 2
3 4
5 6
7 8
If r // s then 1  8
Alternate Exterior Angles Theorem
p
1 2
3 4
r
5 6
7 8
s
If
3
7 then r // s
Corresponding Angles Converse Post.
p
r
s
1 2
3 4
5 6
7 8
If r // s and p  r , then p  s
The Perpendicular Transversal Theorem
Some
Miscellaneous
questions…
Which 2 lines are parallel?
A. y  23 x  1
B. y  32 x  1
C. y  23 x  1
D. y   x  2
3
2
E. y   23 x  1
Which 2 lines are perpendicular?
A. y  3x  1
B. y  32 x  1
C. y  23 x  1
D. y   32 x  2
E. y  32 x  1
What kind of line has a
slope of zero?
Horizontal
Find the slope of the line
containing the points (3,4)
and (0,0):
4
3
Find the slope of the line
containing the points (0,4)
and (0,0):
Undefined
Find the slope of the line
containing the points (-2,5)
and (0,0):
5

2
p
r
s
75o
x
o
=75
p
55o
r
s
x
o
=55
65o
115o= x
p
r
s
45o
x
=135o
110o
r
s
t
60o
70o
Which lines are parallel?
p
110o
r
s
t
60o
70o
Which lines are parallel?
p
70o
Remember the
“Key” to setting up
equations in
Geometry...
You usually do one
of 2 things…
- Set two
expressions equal
to each other
Or….
-Add expressions
together and set
their sum equal to
something else.
Find x
o
6x
o
3x
6x+3x=180
o
6x
x=20
o
3x
FIND X
(3x+10) o
Xo
3x+10+x=90
4x=80
x=20
(3x+10) o =70
X o =20
7x+4
9x-12
Find x
60= 7x+4
9x-12
Find x
= 60
7x+4=9x-12
16=2x
8=x
10x+2
9x-12
Find x
9.
10x+2 =102
9x-12
Find x
=78
10x-2+9x-12=180
19x-10=180
19x=190
x=10
What kind of triangle
has sides of…
4 in. , 6 in. and 3 in.?
SCALENE
What kind of triangle
has Angles of…
o
o
o
90 , 70 , 20 .?
RIGHT
What kind of triangle
has sides of…
5 in. , 5 in. and 3 in.?
ISOSCELES
What kind of triangle
has Angles of…
o
o
o
50 , 60 , 70 .?
ACUTE
What kind of triangle
has Angles of…
o
o
o
60 , 60 , 60 .?
EQUIANGULAR
What kind of triangle
has Angles of…
o
o
o
150 , 10 , 20 .?
OBTUSE
What kind of triangle
has sides of…
5 in. , 5 in. and 5 in.?
EQUILATERAL
What kind of triangle
has Angles of…
o
o
o
150 , 160 , 170 .?
NO SUCH
TRIANGLE
What do we call the
congruent sides of an
Isosceles Triangle?
The LEGS
If D ABC has a right
angle at B, which side
is the Hypotenuse?
A. AB
B. BC
C. AC
Which triangle is Impossible?
• EQUIANGULAR OBTUSE
• SCALENE ISOSCELES
• RIGHT EQUILATERAL
ALL THREE!!
Fill in the blank:
180
m 1  m 2  m 3  _____
2
1
3
Fill in the blank:
m 6
m 1  m 2  _____
5
2
4
1
3
6
Fill in the blank:
m 4
m 3  m 2  _____
5
2
4
1
3
6
Fill in the blank:
m 5
m 3  m 1  _____
5
2
4
1
3
6
When referring to
angle 5, what do we
call 3 and 1 ?
5
REMOTE
INTERIOR
ANGLES
2
4
1
3
6
Fill in the blank:
360
m 4  m 5  m 6  _____
5
2
4
1
3
6
If this triangle is
Equiangular:
60
m 1  _____
2
1
If this triangle is
Equiangular:
2
m 2  120
_____
1
12x-2
7x+3
9x+11
Set up the equation needed to solve the for x:
7 x  3  12 x  2  9 x  11  180
x6
6x+8
12x-19
4x-7
Set up the equation
needed to solve for x:
6 x  8  4 x  7  12 x  19
x  10
7.
50
30
6.
40
100
2.
80 1.
3.
100
60
5.
4.30
80
50
8.
50 8.
1306.
50
5.
9.
70
7.
60
60 4.
50
1.
110
2.
70
50
603.
Given the two triangles
are congruent, complete
the following:
M
TKM
ABC  _______
A
C
T
B
K
Which postulate, if any,
could be used to prove
the triangles are
congruent? I
L
K
SAS
J
M
Which postulate, if any,
could be used to prove
the triangles are
P
congruent?
Q
N
SSS
R
Which postulate, if any,
could be used to prove
the triangles are
congruent?
O
T
NONE
S
V
U
Which postulate, if any,
could be used to prove
the triangles are
congruent? A
D
ASA
B
C
What additional
information is needed to
prove ABC  ZVR
by SSS if
you
already
Know:
BC  VR
AB  ZV
AC  ZR
What additional
information is needed to
prove ABC  ZVR
by SAS if
you
already
Know:
BC  VR
C R
AC  ZR
What additional
information is needed to
prove ABC  ZVR
by ASA if
you
already
Know:
BC  VR
C R
B V
THE END