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First Semester Review 2013

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First Semester Review 2013

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First Semester Review 2013

Points and lines are coplanar if they are together on the same plane.

1. Are B,C and E coplanar?

Yes

2. Are B, C, A, and D coplanar?

No

- Name the plane that is on the bottom of the box.
ex. EFG

- Name the blue plane.
ex. CGH

- Which plane is ADE?
The front

Name two lines that are parallel.

Name two lines that are

skew.

<AOB = 43 and <BOC = 15

What is the measure of <AOC?

<AOB + <BOC = <AOC

43 + 15 = <AOC

58 = <AOC

XZ = 17 and YZ = 11

What is the length of segment XY?

XY + YZ = XZ

XY + 11 = 17

XY = 6

<ABC = 124. Find the measure of x.

Top < + Right < = Total <

<ABD + <DBC = <ABC

(3x+1) + (4x-3) = 124

7x – 2 = 124

7x = 126

x = 18

M is the midpoint of AB. AM = 3x-6 and

MB = 5x-12. Find the measure of x.

3x – 6 = 5x – 12

6 = 2x

3 = x

5x-12

3x-6

When two angles share the same vertex you must use three letters to name the angle.

What is the name of the angle on the left?

<BAC or <CAB

What is the name of the angle on the right?

<CAD or <DAC

C

B

D

A

Use distance and midpoint formulas

Length – 10 units

Midpoint – (0,-1)

(9,8)

The diameter wraps around the circle 3.14 times.

diameter

Since the diameter wraps around the circle 3.14 or π times the formula for perimeter is πd.

The perimeter = 10 π or 31.4

The Area = πr2 = π(5)2 = 25 π or 78.5

Area = 18

Perimeter = 18

If it is August, then it is summertime.

If it is summertime, then it is August.

What is the truth value of this statement?

False

A dog is an animal with a tail.

No

Wednesday is the midpoint of the week.

Yes

February is a month during the year.

No

Ex.Wednesday is the midpoint of the week.

Conditional:Ifit is Wednesday, thenit is the midpoint of the week. (True)

Converse:Ifit is the midpoint of the week, thenit is Wednesday. (True)

Biconditional:It is Wednesday if and only if it is the midpoint of the week.

It is a right angle if and only if it has 90 degrees.

- Ifit is a right angle, thenit has 90 degrees.
- If it has 90 degrees, thenit is a right angle.

Let’s start with an example:

If it is a dog, then it is a mammal.

If it is a mammal, then it is an animal.

By using the Law of Syllogism, we can combine the two sentences. We get:

If it is a dog, then it is an animal.

Example:

If you are in math class, then you are in school.

If you are in Geometry, then you are in math class.

The Law of Syllogism allows us to write the following:

If you are in Geometry, then you are in school.

Don’t think too long when doing this law. It is easier than you think.

Example:

If it is Friday, the lunch room doesn’t serve meat.

“Hey, It’s Friday. What are they serving for lunch?”

… The lunch room isn’t serving meat.

Another example:

If water is frozen, then its temperature is less than 32 degrees.

“There is ice (frozen water) on the pond”

… It’s temperature must be less then 32 degrees.

- <CAD=
- <DAE=
- <CAB=
- <BAF=
- <CAE=

- An angle supplementary to <BAD
- A pair of vertical angles.
- Two angles complementary to <DAE
- An angle adjacent to <CAD

y

3x

x+30

4x+30

y

2x

In Algebra, we use conditionals all the time.

Properties:

Addition Prop of =If a=b, then a+c=b+c

Subtraction Prop of =If a=b, then a–c=b-c

Mult Prop of =If a=b, then

Division Prop of =If a=b, then a/c =b/c

Reflexive Propertya=a

Symmetric PropertyIf a=b, then b=a

Transitive PropertyIf a=b & b=c, then a=c

Substitution PropertyIf a=b, then a can replace b in any expression.

Distributive Property

- <ABC = <ABC
Reflexive Property

- If x + 5 = 11, then x = 6
Subtraction Prop of =

- If x + y = 6 and y = x+2, then x + (x+2) = 6
Substitution Property

- If AB = CD and CD = EF, then AB = EF
Transitive Property

- 5(x – 3) = 5x – 15
Distributive Prop

6.If ½(TR) = 9, then TR = 18

Mult Prop of =

7. If AB = 9, then 9 = AB

Symmetric Prop

Which combination of Reflexive, Symmetric, and Transitive are the following relationships.

… as happy as…

Reflexive, Symmetric, Transitive

… is faster than…

Transitive only

Find the following

- <ABC =
- Complement of <ABC =
- Supplement of <ABC =

Find the following

- <B =
- Supplement of <B =
- Complement of <B =

How big is <A?

<A = 75, the supplement of <A = 15

Corresponding:

Same Side Interior:

Same Side Exterior:

Alternate Interior:

Alternate Exterior:

Parallel lines have …

Perpendicular lines have …

- y = -2xy = -2x + 4
- y = -3/5x + 1y = -3 + 5/3x
- 2x – 3y = 13x – 2y = 8

- 4, 5, 7
- 3, 7, 11
- 5, 10, 15