Conjectures, Counterexamples, and Compound Statements
5, 10, 20, 40, 80, ___, ___, ___
How would you generate the next term of this sequence?
To generate the next term, double the previous term.
Conditional statements are statements that can be written in if - ____ form. What word goes in the blank?
Then
If 3=x, then x=3.
Symmetric Property
The ________ of a line segment divides the segment into 2 congruent parts.
Two angles are _______ if the sum of their measures adds up to 90 degrees.
Complementary
Which of the symbolic notations below would represent a conjunction?
p ^ q or p v q
p ^ q
Conditional, Inverse, Contrapositive and Biconditional are 4 of the 5 types of conditional statements. What is the other type of conditional statement?
Converse Statements
State whether the following conclusion is valid by the Law of Detachment, Law of Syllogism or is invalid.
Given: If Andrew gets all A's, then he will go to the beach.
Given: If Andrew goes to the beach, then he will go surfing.
Conclusion: If Andrew gets all A's, then he will go surfing.
Law of Syllogism
If A, B, and C are collinear points and B is between A and C, what reason allows me to make the following statement:
AB + BC = AC
Segment Addition Postulate
An ______________ divides an angle into two equal parts.
Angle Bisector
Provide a counterexample to the statement below:
Each year has exactly 365 days.
Leap year - 366 days
Which symbolic notation represents the inverse of a conditional statement?
A. q --> p
B. p --> q
C. ~q --> ~p
D. ~p --> ~q
D. ~p --> ~q
Which property of equality is represented by the following statement:
3(x-6) = 3x-18
Distributive Property
If PQ + RS = PS and RS = XY, then PQ + XY = PS. What reason justifies this statement:
A. Symmetric Property
B. Segment Addition Postulate
C. Substitution Property
D. Transitive Property
C. Substitution Property
_________ lines form right angles.
Perpendicular
Using the following statements, state the appropriate statement for the symbolic form of p ^ ~q and provide the truth value of the statement.
p: Thanksgiving is in November
q: Christmas is not in December
Thanksgiving is in November and Christmas is in December. True.
Which Biconditional Statement is true
A. I live in Cloverdale if and only if I live in Indiana
B. It is Thanksgiving if and only if it is November
C. It is Valentine's Day if and only if it is February 14
C. It is Valentine's Day if and only if it is February 14
State whether the conclusion is true by the Law of Detachment, Law of Syllogism or if it's an invalid conclusion.
Given: If you live in Dallas, then you live in Texas.
Given: Morgan does not live in Dallas
Conclusion: Morgan lives in Texas
Invalid Conclusion
If AB = BC, then I can say that B is the midpoint of AC via what reason?
Definition of Midpoint
Given: Angle 1 and Angle 2 are complementary, and Angle 2 and Angle 3 are complementary, what reason allows me to say that Angle 1 is congruent to Angle 3
Congruent Complements Theorem
Provide the correct statement and truth value for the following symbolic form using the statements below: ~p v q
p: Supplementary angles are always congruent
q: Complementary angles are 2 angles that combined equal 180 degrees
Supplementary angles are not always congruent or Complementary angles are 2 angles that combined equal 180 degrees. True
What is the contrapositive of the following conditional statement?
If it is Saturday, then there is no school.
If there is school, then it is not Saturday.
Which property of equality allows me to make the following statement?
If 10a = 2b and 2b = 3c, then 10a = 3c
Transitive Property
If PQ = RS and RS = TU, then what statement can I make using the transitive property?
PQ = TU
Given that angles 1 and 3 form a right angle, what reason allows me to say that angles 1 and 3 are complementary
Complement Theorem