You will be expected to know the definition of the following vocabulary words:
1. Collinear –
P)oints that lie on the same line
2. Coplanar
Points that lie on the same plane
3. Deductive
Reasoining
4. Inductive
Reasoning
5. Intersection
Making predictions about future occurrences based on observed patterns
6. Line
A straight path that extends in opposite directions infinitely
7. Opposite Rays
Two rays that share a common endpoint and extend in opposite directions, forming a line.
8. Plane
A flat surface that extends in all directions.
9. Point
An exact location in space with no size or shape.
10. Ray
A point on a line, and the set of all points extending from one side of that point
11. Segment
A set of two endpoints and all the points that lie between them
12. Skew
Two non-coplanar lines that do not intersect
13. Space
The set of all points in three dimensions
14. Undefined
Terms
15. Counterexample
Points, Lines, and Planes
16. Conditional
Statement
17. Biconditional
Statement
18. Converse
A statement made of a hypothesis and conclusion
IF P, then Q
P IFF Q
19. Inverse
If not P, then Q
20. Contrapositive
If not Q, then not P
21. Negation
Making something opposite
22. Truth Value
A value indicating if a statement/proposition is true or not
23. Two Column
Proof
24. Addition
Property of
Equality
Shows statements and reasons for statements of a proof aligned in two columns
The set of point(s) two or more figures share in common.
An example that proves a statement is false
If Q, then P
If A=C, the A+B=C+B
25. Multiplication
Property of
Equality
26. Division
Property of
Equality
27. Substituiton
Property of
Equality
28. Reflexive
Property of
Equality
29. Distribution
Property of
Equality
30. Law of Syllogism
IF A=C, then A*B=C*B
IF A=C, then A/B=C/B
IF A=B, and A=C, then B=C
A=A
A(B+C)=AB+AC
31. Law of
Detachment
Prove the scenarios given using a two column proof:
32. Given: 3x-4=17
Prove: x=9
Statement
3x-4=17
3x=21
x=7
Reason
Given
Addition Property of Equality
Division Property of Equality
2𝑥+1
33. Given:
=7
3
Prove: x=5
Statement
Reason
(2x+1)/3=7
Given
Multiplication Property of Equality
2x+1=21
Subtraction Property of Equality
2x=20
Division Property of Equality
x=10
Identify the properties of equality represented below:
34. b=b
Reflexive
35. a+b+z=z+a+b
Commutative
36. a(b+c)=ab+ac
Distributive
37.a=x , x=b; a=b
Transitive
Using the Venn diagrams below, write the conditional statements that apply:
38. If it is a carrot, then it is a vegetable
Vegetable
Carrot
39. (there should be three)
a. If they are Jordans, then they are
Shoes
athletic shoes
Athletic Shoes
b. If they are athletic shoes, then they
are shoes
Jordans
c. If they are Jordans, then they are
shoes
40. Complete the Table Below and determine the truth value of each statement:
Conditional
Converse
Inverse
Contrapositive
Bi-Conditional
If they do not
create a point or
line, then three
planes do not
intersect - True
IF three points are
not on the same
line, then they are
not collinear - True
Three planes
intersect IFF they
create a point or a
line - True
If three planes
intersect then
they create a
point or a line
If they create a
point or line, then
three planes
intersect - True
If three planes do
not intersect, then
they do not create a
point or a line - True
If three points are
collinear, then they
lie on the same line.
- True
If three points
are on the same
line then they
are collinear
IF three points are
not collinear, then
they do not lie on
the same line - True
If three points are
not on the same
line, then they are
not coplanar - False
If three points are
not coplanar, then
they are not on the
same line - False
IF three points are
coplanar, then they
lie on the same line
- False
If three points
are coplanar
then they are on
the same line
Three points lie on
the same line IFF
they are coplanar False
IF two lines
intersect, then they
are not skew - True
If they are not
skew, then two
lines intersect False
If two lines do
not intersect,
then they are
skew
If two lines are
skew, then they do
not intersect - True
Two lines are skew
IFF they do not
intersect - False
If two lines
intersect, then they
make a point - True
If two lines make a
point, then they
intersect - True
IF two lines do not
intersect, then they
do not make a point
- true
If two lines to not
make a point, then
they do not
intersect - true
Two lines
intersect IFF they
make a point.
Three points line on
the same line IFF
they are collinear True
41.Determine if the law of syllogism or detachment can be used, if so re-write each
conditional statement:
Statement
If two lines intersect, they
create a point
Line a intersects with line b
If the sun is shining the
students are happy.
If the students are happy,
they work hard.
If a teacher says to be quiet
students pay attention.
If students pay attention, they
learn a lot.
If there are two opposite rays,
they create a line.
⃗⃗⃗⃗⃗ and Ray 𝐵𝐶
⃗⃗⃗⃗⃗ are
Ray 𝐵𝐴
opposite Rays.
Syllogism
Detachment
Line a and b create a point
IF the sun is shining, then the
students work hard
IF a teacher says to be quiet,
then the students learn a lot
Ray ⃗⃗⃗⃗⃗
𝐵𝐴 and Ray ⃗⃗⃗⃗⃗
𝐵𝐶 create a
line.
42.Using the Diagram provided, determine what you know is fact and what you can assume
from the choices below:
a. There is a horse
b. There is a human
c. The human is holding a sword
d. The human is holding a shield
e. The horse is running
f. The human is fighting someone
Assumption:
Fact:
e, f
a, b, c, d
43.Determine if the statements are true, if false, provided a counter example:
If two rays share an end point, then they are
opposite rays
False
If two lines do not intersect, then they are
parallel
If there is a Ray that has endpoint A and goes
through point B, the ray is named as ⃡⃗⃗⃗⃗
𝐴𝐵
False
Counter Example
Two rays that share an
endpoint can make an angle
Skew lines
False
⃗⃗⃗⃗⃗
𝐴𝐵
44.Using the diagram provided determine if the statements are true or false:
Statement
⃡⃗⃗⃗⃗
𝐴𝐵𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑠 ⃡⃗⃗⃗⃗
𝐶𝐷 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡 𝐶
Points G and E are collinear
𝑙𝑖𝑛𝑒 ℎ 𝑖𝑠 𝑠𝑘𝑒𝑤 𝑡𝑜 ⃡⃗⃗⃗⃗
𝐾𝐹
True False
True False
True False