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.
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Points and lines are coplanar if they are together on the same plane.
1. Are B,C and E coplanar?
2. Are B, C, A, and D coplanar?
Name two lines that are parallel.
Name two lines that are
<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
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
Use distance and midpoint formulas
Length – 10 units
Midpoint – (0,-1)
The diameter wraps around the circle 3.14 times.
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?
A dog is an animal with a tail.
Wednesday is the midpoint of the week.
February is a month during the year.
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.
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.
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.
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.
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.
In Algebra, we use conditionals all the time.
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 Property a=a
Symmetric Property If a=b, then b=a
Transitive Property If a=b & b=c, then a=c
Substitution Property If a=b, then a can replace b in any expression.
Subtraction Prop of =
6. If ½(TR) = 9, then TR = 18
Mult Prop of =
7. If AB = 9, then 9 = AB
Which combination of Reflexive, Symmetric, and Transitive are the following relationships.
… as happy as…
Reflexive, Symmetric, Transitive
… is faster than…
Find the following
Find the following
How big is <A?
<A = 75, the supplement of <A = 15
Same Side Interior:
Same Side Exterior:
Parallel lines have …
Perpendicular lines have …