Exploring Inductive Reasoning and Conjectures in Geometry

What is the primary purpose of inductive reasoning in mathematics?

• To solve equations

• To arrive at a conclusion based on examples

• To prove theorems directly

• To memorize formulas

In the sequence 2, 5, 8, 11, 14, what is the next term?

• 19

• 17

• 16

• 18

If the pattern in the sequence 5, -5, -20, -40 is identified, what is the next term?

• -55

• -60

• -65

• -50

What is the conjecture for the sequence 1, 1, 2, 3, 5, 8?

• Each term is the difference of the previous two terms

• Each term is the quotient of the previous two terms

• Each term is the sum of the previous two terms

• Each term is the product of the previous two terms

If angle MNP is a right angle, what can be said about its measure?

• It is 45 degrees

• It is 60 degrees

• It is 90 degrees

• It is 120 degrees

If point B is between points A and C, what can be said about the segments AB and BC?

• AB * BC = AC

• AB - BC = AC

• AB + BC = AC

• AB / BC = AC

What is a counterexample?

• An example that partially supports a conjecture

• An example that is irrelevant to a conjecture

• An example that disproves a conjecture

• An example that supports a conjecture

Which of the following is a counterexample to the statement 'The sum of any two integers is positive'?

• 2 + 3

• -4 + (-2)

• -4 + 2

• 4 + 5

If two lines are perpendicular, what type of angles do they form?

• Straight angles

• Acute angles

• Obtuse angles

• Right angles

If points Q, R, and S are collinear, what must be true about the segments QR and RS?

• QR * RS = QS

• QR - RS = QS

• QR / RS = QS

• QR + RS = QS