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

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 1 2 180m m

The Supplement Theorem

(The angles in a linear pair are supplementary.)

1 2Then

1 2

The Vertical Angles Theorem:

Vertical Angles are congruent.

If and are right angles,

then

A B

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+254x -1

Find x

Answer:

8x+25 + 4x - 1 = 180

12x+24=180

12x=156

x=13

7x-10 5x+12

Find x

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 and are supplementary,

then

A B

180m A m B

The Definition of Supplementary

Angles

If

then

is a right angle.

90m AA

The Definition of Right Angle

1

If

is a right angle, then the lines are perpendicular.

1

The Definition of Perpendicular

lines.

If and are complementary, and and are complementary, then

AA

B

C

B C

Congruent Complements Theorem: If 2 angles are complementary to the same angle, they are congruent to each other.

If and are complementary,

then

A B

90m A m B

The Definition of

Complementary Angles

The Supplement Theorem:

The angles in a _____ ____ are supplementary.

x y

Linear Pair

_______ angles are congruent.

Vertical

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, ____________ intersect to form right angles.

Perpendicular lines

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

r

s

p

1

6

23 4

57 8

, // .If p r and p s then r s The Perpendicular Transversal Converse

Theorem

1

6

23 4

57 8

3 6 //If then r s Alternate Interior Angles Converse

Theorem

r

s

r

s

p

1

6

23 4

57 8

// 4 6 180If r s then m m Consecutive Interior Angles

Theorem

r

s

p

1

6

23 4

57 8

// 4 8If r s then m m Corresponding Angles Postulate

r

s

p

1

6

23 4

57 8

7 8 180m m

The Supplement Theorem

1

6

23 4

57 8

2 7 //If then r s Alternate Exterior Angles Converse

Theorem

r

s

r

s

p

1

6

23 4

57 8

5 8 Vertical Angles Theorem

r

s

p

1

6

23 4

57 8

3 5 180 //If m then r s Consecutive Interior Angles Converse

Theorem

r

s

p

1

6

23 4

57 8

// 1 8If r s then Alternate Exterior Angles Theorem

r

s

p

1

6

23 4

57 8

3 7 //If then r s Corresponding Angles Converse Post.

r

s

p

1

6

23 4

57 8

// ,If r s and p r then p s The Perpendicular Transversal Theorem

Some Miscellaneous questions…

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

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

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

r

s

p

x

75o

=75o

r

s

p

x

=55o

55o

x

65o

115o=

r

s

p

x

45o

=135o

r

s

t

p110o

60o

70o

Which lines are parallel?

r

s

t

p110o

60o

70o

Which lines are parallel?

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

3xo6xo

6x+3x=180

x=20

3xo6xo

(3x+10) o

X o

FIND X

(3x+10) o

X o

3x+10+x=90

4x=80

x=20=70

=20

7x+4

9x-12

Find x

7x+4

9x-12

Find x 7x+4=9x-12

16=2x

8=x

60=

= 60

9x-12

Find x

10x+2

9.

9x-12

Find x

10x+2

10x-2+9x-12=180

19x-10=180

19x=190

x=10

=102

=78

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

What kind of What kind of triangle has triangle has AnglesAngles of… of…

9090oo, 70, 70oo, , 2020oo.?.? RIGHT


5 in. , 5 in. and 3 5 in. , 5 in. and 3 in.?in.?ISOSCELES


5050oo, 60, 60oo, , 7070oo.?.?ACUTE


6060oo, 60, 60oo, , 6060oo.?.?EQUIANGULAR


150150oo, 10, 10oo, , 2020oo.?.?OBTUSE


5 in. , 5 in. and 5 5 in. , 5 in. and 5 in.?in.?EQUILATERAL


150150oo, 160, 160oo, , 170170oo.?.?

NO SUCH TRIANGLE

What do we call What do we call the congruent the congruent sides of an sides of an Isosceles Isosceles Triangle?Triangle?The LEGS

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

Which triangle is Which triangle is Impossible?Impossible?

•EQUIANGULAR OBTUSE•SCALENE ISOSCELES•RIGHT EQUILATERAL

ALL THREE!!

Fill in the blank:Fill in the blank:

1 2 3 _____m m m

2

31

180

6

5

4

2

3

1

Fill in the blank:Fill in the blank:1 2 _____m m 6m

6

5

4

2

3

1


6

5

4

2

3

1


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

6

5

4

2

3

1

Fill in the blank:Fill in the blank:4 5 6 _____m m m 360

If this triangle is If this triangle is Equiangular:Equiangular:

1 _____m 60 2

1

If this triangle is If this triangle is Equiangular:Equiangular:

2 _____m 120 2

1

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

12x-19

4x-76x+8

Set up the equation needed to solve for x:

6 8 4 7 12 19x x x

10x

80

100

100

8.7.

6.

5.4.

3.

2.1. 80

503060

40

50 30

9.8. 7.

6. 5. 4.

3.

2.1.

110

50

50

70

60

6050130

6050

70

A

M

KT

B

C

Given the two triangles are congruent, complete the following:

_______ABC TKM

Which postulate, if any, could be used to prove the triangles are congruent?

M

LI

K

J

SAS

Q

R

N

P


SSS

T

S

O U

V


NONE

C

A

B

D

ASA


ABC ZVR

BC VRAB ZV

What additionalinformation is needed to prove

by SSS if you already Know: AC ZR

ABC ZVR

BC VRC R


by SAS if you already Know: AC ZR

ABC ZVR

BC VRC R


by ASA if you already Know: B V

THE END

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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