You will be expected to know the definition of the following vocabulary words:

  1. Collinear –
/ P)oints that lie on the same line
  1. Coplanar
/ Points that lie on the same plane
  1. Deductive Reasoining

  1. Inductive Reasoning
/ Making predictions about future occurrences based on observed patterns
  1. Intersection
/ The set of point(s) two or more figures share in common.
  1. Line
/ A straight path that extends in opposite directions infinitely
  1. Opposite Rays
/ Two rays that share a common endpoint and extend in opposite directions, forming a line.
  1. Plane
/ A flat surface that extends in all directions.
  1. Point
/ An exact location in space with no size or shape.
  1. Ray
/ A point on a line, and the set of all points extending from one side of that point
  1. Segment
/ A set of two endpoints and all the points that lie between them
  1. Skew
/ Two non-coplanar lines that do not intersect
  1. Space
/ The set of all points in three dimensions
  1. Undefined Terms
/ Points, Lines, and Planes
  1. Counterexample
/ An example that proves a statement is false
  1. Conditional Statement
/ A statement made of a hypothesis and conclusion
IF P, then Q
  1. Biconditional Statement
/ P IFF Q
  1. Converse
/ If Q, then P
  1. Inverse
/ If not P, then Q
  1. Contrapositive
/ If not Q, then not P
  1. Negation
/ Making something opposite
  1. Truth Value
/ A value indicating if a statement/proposition is true or not
  1. Two Column Proof
/ Shows statements and reasons for statements of a proof aligned in two columns
  1. Addition Property of Equality
/ If A=C, the A+B=C+B
  1. Multiplication Property of Equality
/ IF A=C, then A*B=C*B
  1. Division Property of Equality
/ IF A=C, then A/B=C/B
  1. Substituiton Property of Equality
/ IF A=B, and A=C, then B=C
  1. Reflexive Property of Equality
/ A=A
  1. Distribution Property of Equality
/ A(B+C)=AB+AC
  1. Law of Syllogism

  1. Law of Detachment

Prove the scenarios given using a two column proof:

  1. Given: 3x-4=17
/
  1. Given:

Prove: x=9 / Prove: x=5
Statement / Reason / Statement / Reason
3x-4=17 / Given / (2x+1)/3=7 / Given
3x=21 / Addition Property of Equality / 2x+1=21 / Multiplication Property of Equality
x=7 / Division Property of Equality / 2x=20 / Subtraction Property of Equality
x=10 / Division Property of Equality

Identify the properties of equality represented below:

  1. b=b
Reflexive /
  1. a+b+z=z+a+b
Commutative
  1. a(b+c)=ab+ac
Distributive /
  1. a=x , x=b; a=b
Transitive

Using the Venn diagrams below, write the conditional statements that apply:

  1. If it is a carrot, then it is a vegetable
/

  1. (there should be three)
  1. If they are Jordans, then they are athletic shoes
  2. If they are athletic shoes, then they are shoes
  3. If they are Jordans, then they are shoes
/


  1. Complete the Table Below and determine the truth value of each statement:

Conditional / Converse / Inverse / Contrapositive / Bi-Conditional
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 they do not create a point or line, then three planes do not intersect - True / Three planes intersect IFF they 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 collinear - True / Three points line on the same line IFF they are collinear - 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.
  1. Determine if the law of syllogism or detachment can be used, if so re-write each conditional statement:

Statement / Syllogism / Detachment
If two lines intersect, they create a point
Line a intersects with line b / Line a and b create a point
If the sun is shining the students are happy.
If the students are happy, they work hard. / IF the sun is shining, then the students work hard
If a teacher says to be quiet students pay attention.
If students pay attention, they learn a lot. / IF a teacher says to be quiet, then the students learn a lot
If there are two opposite rays, they create a line.
Ray and Ray are opposite Rays. / Ray and Ray create a line.
  1. Using the Diagram provided, determine what you know is fact and what you can assume from the choices below:

  1. There is a horse
  2. There is a human
  3. The human is holding a sword
  4. The human is holding a shield
  5. The horse is running
  6. The human is fighting someone

Assumption: / Fact:
e, f / a, b, c, d
  1. 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 / Counter Example
Two rays that share an endpoint can make an angle
If two lines do not intersect, then they are parallel / False / Skew lines
If there is a Ray that has endpoint A and goes through point B, the ray is named as / False /
  1. Using the diagram provided determine if the statements are true or false:

Statement /
/ True False
Points G and E are collinear / True False
/ True False