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 are skew.

Segment and Angle addition postulates <AOB = 43 and <BOC = 15 What is the measure of <AOC? <AOB + <BOC = <AOC = <AOC 58 = <AOC

Segment and Angle addition postulates XZ = 17 and YZ = 11 What is the length of segment XY? XY + YZ = XZ XY + 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 – 12 6 = 2x 3 = x 3x-6 5x-12

Naming an Angle 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 D C B A

Review – Find the length and midpoint of AB Use distance and midpoint formulas Length – 10 units Midpoint – (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 = πr 2 = π(5) 2 = 25 π or 78.5

Find the area and perimeter of the shape. Area = 18 Perimeter = 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 Syllogism 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.

Sometimes the sentences are reversed BE 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 Detachment 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.

Law of Detachment 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.

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. 3x y x+30

Find the measure of x and y. 2x 4x+30 y

Properties of Equality 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

More Properties 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

Identifying the Properties 1.<ABC = <ABC Reflexive 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) = 6 Substitution Property 4.If AB = CD and CD = EF, then AB = EF Transitive Property

Identifying More Properties 5.5(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

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. 2The 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?

Label each type of angle as congruent or supplementary, when lines are parallel Corresponding: 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 = -2xy = -2x y = -3/5x + 1y = /3x 3.2x – 3y = 13x – 2y = 8

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, , 10, 15

What type of dividing line is each of the following?