go to the head of the class-- review game. rules: a question starts with a player. if that player...
TRANSCRIPT
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Go To The Head of the Class--Review Game
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Rules: A question starts with a player. If that player answers correctly he/she keeps his/her seat.
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If the player misses, then the question goes to the next player. If missed, it goes to the next player...
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…and continues until someone gets it correct. That student moves to the seat where the question started...
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…and everyone who missed the question moves back one seat.
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The object of the game is to occupy and keep the #1 seat.
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Questions with a limited number of possible responses will not be offered indefinitely. A substitute question will be posed.
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It is important to listen to previous responses. They will not be repeated for you.
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The first person to receive a question will have a maximum of 30 seconds to answer.
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Every person after that has only 10 seconds to reply.
Be ready when called upon.
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If the question is on a yellow screen, expect to solve a problem.
Have calculator, paper & pencil ready.
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If the background is orange, name the definition, property, theorem, etc, that supports the given conclusion.
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If the question is on a green screen, it requires just a short answer.
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Time to Play:
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READY?
(begin)
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1 2
Then 1 2 180m m
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The Supplement Theorem
(The angles in a linear pair are supplementary.)
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1 2Then
1 2
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The Vertical Angles Theorem:
Vertical Angles are congruent.
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If and are right angles,
then
A B
A B
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The Right Angle Theorem: All Right
angles are congruent.
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Two angles are complementary. One is 32 degrees. What is the measure of the other one?
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ANSWER:
58 degrees
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What do we call 2 non-adjacent angles that are formed when 2 lines intersect?
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Answer:
Vertical Angles
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Two angles are supplementary. One angle is 73 degrees, find the measure of the other one.
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Answer:
107 degrees
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What do we call 2 lines that intersect to form right angles?
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Answer:
Perpendicular Lines
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Complete this theorem:
If 2 angles are complementary to the same angle…...
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Answer:
… then they are congruent to each other.
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Remember the “Key” to setting up equations in Geometry...
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You usually do one of 2 things…
- Set two expressions equal to each other
Or….
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-Add expressions together and set their sum equal to something else.
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8x+254x -1
Find x
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Answer:
8x+25 + 4x - 1 = 180
12x+24=180
12x=156
x=13
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7x-10 5x+12
Find x
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Answer:
7x-10 = 5x + 12
2x-10 = 12
2x = 22
x = 11
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According to the Supplement Theorem, what kind of angles are supplementary?
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Answer:
The angles in a Linear Pair
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Complete this Theorem:
If 2 lines intersect to form congruent adjacent angles, then….
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…then the lines are perpendicular.
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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.
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Answer: Angle C is 30 degrees.
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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.
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Answer: Angle C is 130 degrees.
A= 40 => B= 50
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If and are supplementary,
then
A B
180m A m B
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The Definition of Supplementary
Angles
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If
then
is a right angle.
90m AA
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The Definition of Right Angle
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1
If
is a right angle, then the lines are perpendicular.
1
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The Definition of Perpendicular
lines.
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If and are complementary, and and are complementary, then
AA
B
C
B C
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Congruent Complements Theorem: If 2 angles are complementary to the same angle, they are congruent to each other.
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If and are complementary,
then
A B
90m A m B
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The Definition of
Complementary Angles
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The Supplement Theorem:
The angles in a _____ ____ are supplementary.
x y
Linear Pair
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_______ angles are congruent.
Vertical
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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
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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.
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+ = 180
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According to their definition, ____________ intersect to form right angles.
Perpendicular lines
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What term describes the two lines? Parallel
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What term describes the two lines? Skew
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Identify the type of angles pictured
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Corresponding Angles
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Alternate Exterior Angles
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Consecutive Interior Angles
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Alternate Interior Angles
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Vertical Angles
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Corresponding Angles
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A Linear Pair
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r
s
p
1
6
23 4
57 8
, // .If p r and p s then r s The Perpendicular Transversal Converse
Theorem
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1
6
23 4
57 8
3 6 //If then r s Alternate Interior Angles Converse
Theorem
r
s
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r
s
p
1
6
23 4
57 8
// 4 6 180If r s then m m Consecutive Interior Angles
Theorem
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r
s
p
1
6
23 4
57 8
// 4 8If r s then m m Corresponding Angles Postulate
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r
s
p
1
6
23 4
57 8
7 8 180m m
The Supplement Theorem
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1
6
23 4
57 8
2 7 //If then r s Alternate Exterior Angles Converse
Theorem
r
s
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r
s
p
1
6
23 4
57 8
5 8 Vertical Angles Theorem
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r
s
p
1
6
23 4
57 8
3 5 180 //If m then r s Consecutive Interior Angles Converse
Theorem
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r
s
p
1
6
23 4
57 8
// 1 8If r s then Alternate Exterior Angles Theorem
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r
s
p
1
6
23 4
57 8
3 7 //If then r s Corresponding Angles Converse Post.
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r
s
p
1
6
23 4
57 8
// ,If r s and p r then p s The Perpendicular Transversal Theorem
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Some Miscellaneous questions…
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Which 2 lines are parallel?
23
32
23
32
23
. 1
. 1
. 1
. 2
. 1
A y x
B y x
C y x
D y x
E y x
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Which 2 lines are perpendicular?
32
23
32
32
. 3 1
. 1
. 1
. 2
. 1
A y x
B y x
C y x
D y x
E y x
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What kind of line has a slope of zero?
Horizontal
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Find the slope of the line containing the points (3,4) and (0,0):
4
3
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Find the slope of the line containing the points (0,4) and (0,0):
Undefined
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Find the slope of the line containing the points (-2,5) and (0,0):
5
2
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r
s
p
x
75o
=75o
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r
s
p
x
=55o
55o
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x
65o
115o=
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r
s
p
x
45o
=135o
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r
s
t
p110o
60o
70o
Which lines are parallel?
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r
s
t
p110o
60o
70o
Which lines are parallel?
70o
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Remember the “Key” to setting up equations in Geometry...
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You usually do one of 2 things…
- Set two expressions equal to each other
Or….
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-Add expressions together and set their sum equal to something else.
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Find x
3xo6xo
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6x+3x=180
x=20
3xo6xo
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(3x+10) o
X o
FIND X
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(3x+10) o
X o
3x+10+x=90
4x=80
x=20=70
=20
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7x+4
9x-12
Find x
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7x+4
9x-12
Find x 7x+4=9x-12
16=2x
8=x
60=
= 60
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9x-12
Find x
10x+2
9.
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9x-12
Find x
10x+2
10x-2+9x-12=180
19x-10=180
19x=190
x=10
=102
=78
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What kind of What kind of triangle has triangle has sidessides of…of…
4 in. , 6 in. and 3 4 in. , 6 in. and 3 in.?in.?SCALENE
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
9090oo, 70, 70oo, , 2020oo.?.? RIGHT
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What kind of What kind of triangle has triangle has sidessides of…of…
5 in. , 5 in. and 3 5 in. , 5 in. and 3 in.?in.?ISOSCELES
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
5050oo, 60, 60oo, , 7070oo.?.?ACUTE
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
6060oo, 60, 60oo, , 6060oo.?.?EQUIANGULAR
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
150150oo, 10, 10oo, , 2020oo.?.?OBTUSE
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What kind of What kind of triangle has triangle has sidessides of…of…
5 in. , 5 in. and 5 5 in. , 5 in. and 5 in.?in.?EQUILATERAL
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
150150oo, 160, 160oo, , 170170oo.?.?
NO SUCH TRIANGLE
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What do we call What do we call the congruent the congruent sides of an sides of an Isosceles Isosceles Triangle?Triangle?The LEGS
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If If ABC has a ABC has a right angle at B, right angle at B, which side is the which side is the Hypotenuse?Hypotenuse?. . .A AB B BC C AC
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Which triangle is Which triangle is Impossible?Impossible?
•EQUIANGULAR OBTUSE•SCALENE ISOSCELES•RIGHT EQUILATERAL
ALL THREE!!
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Fill in the blank:Fill in the blank:
1 2 3 _____m m m
2
31
180
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:1 2 _____m m 6m
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:3 2 _____m m 4m
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:3 1 _____m m 5m
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6
5
4
2
3
1
When referring to When referring to angle 5, what do angle 5, what do we call we call ? ?
3 1and
REMOTE INTERIOR ANGLES
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:4 5 6 _____m m m 360
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If this triangle is If this triangle is Equiangular:Equiangular:
1 _____m 60 2
1
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If this triangle is If this triangle is Equiangular:Equiangular:
2 _____m 120 2
1
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9x+11
12x-2
7x+3
Set up the equation needed to solve the for x:
7 3 12 1 1 01 82 9x x x 6x
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12x-19
4x-76x+8
Set up the equation needed to solve for x:
6 8 4 7 12 19x x x
10x
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80
100
100
8.7.
6.
5.4.
3.
2.1. 80
503060
40
50 30
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9.8. 7.
6. 5. 4.
3.
2.1.
110
50
50
70
60
6050130
6050
70
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A
M
KT
B
C
Given the two triangles are congruent, complete the following:
_______ABC TKM
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Which postulate, if any, could be used to prove the triangles are congruent?
M
LI
K
J
SAS
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Q
R
N
P
Which postulate, if any, could be used to prove the triangles are congruent?
SSS
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T
S
O U
V
Which postulate, if any, could be used to prove the triangles are congruent?
NONE
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C
A
B
D
ASA
Which postulate, if any, could be used to prove the triangles are congruent?
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ABC ZVR
BC VRAB ZV
What additionalinformation is needed to prove
by SSS if you already Know: AC ZR
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ABC ZVR
BC VRC R
What additionalinformation is needed to prove
by SAS if you already Know: AC ZR
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ABC ZVR
BC VRC R
What additionalinformation is needed to prove
by ASA if you already Know: B V
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THE END