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
DOUBLE POINT QUESTION!
What property of equality is represented by this statement?
If 3=x, then x=3.
Symmetric Property
The ________ of a line segment divides the segment into 2 congruent parts.
DOUBLE POINT QUESTION!
Two angles are _______ if the sum of their measures adds up to 90 degrees.
Complementary
Which of the symbolic notations below would represent a conditional statement?
p -> q or q -> p
p -> q
DOUBLE POINT QUESTION!
Conditional, Inverse, Contrapositive and Bi-conditional 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 Property of Equality
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
DOUBLE POINT QUESTION!
a. Identify the hypothesis and conclusion
b. Provide a counterexample
If a figure has four sides, then it is a rectangle.
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 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
D. Transitive Property
_________ lines form right angles.
Perpendicular
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 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
Solve the equation. Justify each step.
5(3x - 20) = -10
x = 6
Distributive property, Addition property of =, Division property of =
DOUBLE POINT QUESTION!
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
True or false? If false, provide a counterexample.
Supplementary angles are always congruent.
False, ex. 130 & 50
a. What is the converse of the following conditional statement?
b. Is the converse true or false?
If it is Saturday, then there is no school.
a. If there is no school, then it is Saturday.
b. False, it could be Sunday, summer, vacation, etc.
DOUBLE POINT QUESTION!
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
Definition of Complementary