First Semester Review 2013

ColLinear & CoPlanar

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

Quick Review• 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

Finding Parallel and skew lines

Name two lines that are parallel.

Name two lines that areskew.

Segment and Angle addition postulates<AOB = 43 and <BOC = 15What is the measure of <AOC?

<AOB + <BOC = <AOC 43 + 15 = <AOC

58 = <AOC

Segment and Angle addition postulatesXZ = 17 and YZ = 11What is the length of segment XY?

XY + YZ = XZXY + 11 = 17

XY = 6

Segment and Angle addition postulates<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

Midpoints

M is the midpoint of AB. AM = 3x-6 and MB = 5x-12. Find the measure of x.

3x – 6 = 5x – 126 = 2x3 = x

3x-6

5x-12

Naming an AngleWhen 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

D

CB

A

Review – Find the length and midpoint of AB

Use distance and midpoint formulas

Length – 10 unitsMidpoint – (0,-1)

In the picture, find the missing endpoint.

(9,8)

Why does the distance around a circle = πd?The diameter wraps around the circle 3.14 times.

diameter

Find the area and perimeter of the shape.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

Find the area and perimeter of the shape.

Area = 18Perimeter = 18

Write the converse for the statement.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

Are the following definitions good definitions?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

Example of a Biconditional

Ex. Wednesday is the midpoint of the week.Conditional: If it is Wednesday, then it is the midpoint of the week. (True)Converse: If it is the midpoint of the week, then it is Wednesday. (True)

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

Working backwards – Write the biconditional as two sentences.

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

1. If it is a right angle, then it has 90 degrees.2. If it has 90 degrees, then it is a right angle.

Law of SyllogismLet’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.

Sometimes the sentences are reversedBE CAREFUL!

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.

Law of DetachmentDon’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.

Law of DetachmentAnother 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.

Find the measure of the angles

1. <CAD =2. <DAE =3. <CAB =4. <BAF =5. <CAE =

Naming Angles

1. An angle supplementary to <BAD

2. A pair of vertical angles.

3. Two angles complementary to <DAE

4. An angle adjacent to <CAD

Find x and y.

3xy

x+30

Find the measure of x and y.

2x

4x+30y

Properties of Equality

In Algebra, we use conditionals all the time.Properties:Addition Prop of = If a=b, then a+c=b+cSubtraction Prop of = If a=b, then a–c=b-c Mult Prop of = If a=b, thenDivision Prop of = If a=b, then a/c =b/c

a c b c

More PropertiesReflexive Property a=aSymmetric Property If a=b, then b=aTransitive Property If a=b & b=c, then a=cSubstitution Property If a=b, then a can

replace b in any expression.

Distributive Property ( )a b c ab ac

Identifying the Properties

1. <ABC = <ABCReflexive Property

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

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

4. If AB = CD and CD = EF, then AB = EFTransitive Property

Identifying More Properties

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

6. If ½(TR) = 9, then TR = 18Mult Prop of =

7. If AB = 9, then 9 = ABSymmetric Prop

Reflexive, Symmetric, Transitive

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

… as happy as…Reflexive, Symmetric, Transitive… is faster than…Transitive only

Ex. 1 <ABC is 35 degrees.

Find the following

• <ABC =

• Complement of <ABC =

• Supplement of <ABC =

Ex. 2 The supplement of <B is 100

Find the following

• <B =

• Supplement of <B =

• Complement of <B =

Ex. 3 <A is 5 times as big is supplement.How big is <A?

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

Graph y = -1/3x - 2

Graph y = 3

Graph x = 4

Graph y – 2 = 2(x-1)

Write an equation going through (4,1) with a slope of 3. Then graph it.

Write an equation going through (-2,3) with a slope of 1/2. Then graph it.

Find the equation of a line parallel to y = 2x+1 that goes through (3,1)

Find x. What type of angles are these?

Find x. What type of angles are these?

Find x. What type of angles are these?

Label each type of angle as congruent or supplementary, when lines are parallelCorresponding:

Same Side Interior:

Same Side Exterior:

Alternate Interior:

Alternate Exterior:

Find x. What type of angles are these?

How do you know if two lines parallel, perpendicular or neither based on their slopes?

Parallel lines have …

Perpendicular lines have …

Are the lines parallel, perpendicular, or neither?1. y = -2x y = -2x + 4

2. y = -3/5x + 1 y = -3 + 5/3x

3. 2x – 3y = 1 3x – 2y = 8

Which Triangle Congruence postulate would we use to show the triangles are congruent?

Which Triangle Congruence postulate would we use to show the triangles are congruent?

Find x. What type of problem is this?

Do the following sides make a triangle?1. 4, 5, 7

2. 3, 7, 11

3. 5, 10, 15

What type of dividing line is each of the following?