Reasoning
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
What property of equality is represented by this statement?
If 3=x, then x=3.
Symmetric POE
The ________ of a line segment divides the segment into 2 congruent parts.
Which of the symbolic notations below would represent a conditional statement?
a.) p -> q
b.) q -> p
c.) p<->q
a.) 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
Identify the property that is used to solve the equation:
6x = 42
Division POE
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
If a figure has four sides, then it is a rectangle.
a.) Identify the hypothesis and conclusion
b.) Provide a counterexample
p= a figure has four sides
q= it is a rectangle
Counterexample: rhombus, parallelogram, kite, etc.
Write the statements as a biconditional:
If you can vote, then you are at least 18 years old. If you are at least 18 years old, then you can vote.
You can vote if and only if you are at least 18 years old.
Which property of equality is represented by the following statement:
3(x-6) = 3x-18
Distributive POE
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.) Addition Property
C.) Substitution Property
Provide a counterexample to show that the conjecture is false:
If two angles are supplements of each other, then one of the angles must be acute.
Both are right angles/ 90 degree angles.
Which Biconditional Statement is true
A.) I live in Boston if and only if I live in MA
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
Solve the equation. Justify each step.
5(3x - 20) = -10
5(3x - 20) = -10 Given
15x-100=-10 Distributive POE
15x=90 Addition POE
x = 6 Division POE
DOUBLE POINT QUESTION!
If AB = BC, then I can say that B is the midpoint of AC via what reason?
Definition of Midpoint
True or false? If false, provide a counterexample.
Supplementary angles are always congruent.
False, ex. 130 & 50
If it is Saturday, then there is no school.
a.) What is the converse of the following conditional statement?
b.) Is the converse true or false?
a.) If there is no school, then it is Saturday.
b.) False, it could be Sunday, summer, vacation, etc.
Which property of equality allows me to make the following statement?
If 10a = 2b and 2b = 3c, then 10a = 3c
Transitive POE
If PQ = RS and RS = TU, then what statement can I make using the transitive property?
PQ = TU