Patterns and Inductive Reasoning
Find the next two terms in the sequence: 81, 27, 9, 3, ___, ___.
1 and 1/3
Rewrite the statement as a conditional statement. "All motorcyclists wear helmets."
"Someone who is a motorcyclist, wears a helmet."
Identify the property: if a=b and b=c, then a=c.
The transitive property
If ray XP bisects <QXZ, how would you justify the statement: m<QXP = m<PXZ?
The definition of angle bisector
What are the next two terms of the sequence 34, 27, 20, 13, ___, ___?
6 and 1
Write the Converse of the conditional and determine if it is true or false. If false give a counterexample. "If you play the tuba, then you play an instrument."
"If you play an instrument, then you play the tuba. (FALSE, you could play any other instrument.)
The process of using observed patterns to make a conjecture.
What is inductive reasoning.
Identify the property: if a = b, then a - c = b - c.
The subtraction property of equality
If segment AB is CONGRUENT to segment CD, how would you justify the statement: AB=CD?
The definition of congruence
Find the pattern of the sequence: 1, 4, 9, 16, 25.
Each term is the square of the number of the term in the sequence.
Is the conditional statement true or false? If it is false, find a counterexample. "If a woman is born in Florida, then she is American."
True
Identify the property: a = a.
The reflexive property of equality
When you replace a value with another value, what property are you using?
Substitution property of =
A _________ is a conclusion you reach using inductive reasoning.
A conjecture
Write the Inverse of the conditional and determine if it is true or false. If false give a counterexample. "If you play the tuba, then you play an instument."
"If you do not play the tuba, then you do not play an instrument." (FALSE, you could play any other instrument.)
A Postulate does not need ______________.
proof
Identify the property: if a = b then b = a.
The symmetric property of equality
If C is the midpoint a of DE, then DC is congruent to CE. What is the reason that we can say so?
Definition of Midpoint
Find a counterexample to show the following statement is false. "If the name of a month starts with the letter J, it is a summer month."
January
The point that divides a segment into two congruent segments.
The midpoint
Identify the property: if B is between A and C on segment AC, then AC = AB + BC?
The Segment Addition Postulate.
In this property, we eliminate the "middleman."
If A + B = 90, and C + D = 90, THEN A + B = C + D
Transitive Property of Equality