Patterns and Inductive Reasoning

Conditional Statements

Definitions

Algebraic Proof

Geometry Proof

100

Find the next two terms in the sequence: 81, 27, 9, 3, ___, ___.

1 and 1/3

100

Rewrite the statement as a conditional statement. "All motorcyclists wear helmets."

"Someone who is a motorcyclist, wears a helmet."

100

A statement that can be written in the form "if p, then q.

What is conditional statement.

100

Identify the property: if a=b and b=c, then a=c.

The transitive property

100

If ray XP bisects <QXZ, how would you justify the statement: m<QXP = m<PXZ?

The definition of angle bisector

200

What are the next two terms of the sequence 34, 27, 20, 13, ___, ___?

6 and 1

200

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.)

200

The process of using observed patterns to make a conjecture.

What is inductive reasoning.

200

Identify the property: if a = b, then a - c = b - c.

The subtraction property of equality

200

If segment AB is congruent to segment CD, how would you justify the statement: AB=CD?

The definition of congruent

300

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.

300

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

300

An argument that uses logic to show that a conclusion is true.

What is a proof.

300

Identify the property: a = a.

The reflexive property of equality

300

When you make a replacement you are doing?

Substitution

400

A _________ is a conclusion you reach using inductive reasoning.

A conjecture

400

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.)

400

A "good definition" is always ______________.

reversible

400

Identify the property: if a = b then b = a.

The symmetric property of equality

400

Define Linear Pair.

A pair of angles that are adjacent and supplementary.

500

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

500

The inverse of the following conditional statement "if you are a quarterback, then you play football.

What is "If you are not a quarterback, then you do not play football.

500

The point that divides a segment into two congruent segments.

The midpoint

500

Identify the property: if B is between A and C on segment AC, then AC = AB + BC?

The Segment Addition Postulate.

500

Which property shows up in almost every proof we do?

The Transitive Property of Equality

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