Inductive and Deductive Reasoning in Geometry

What is a conjecture in the context of inductive reasoning?

• A proven statement based on observations

• An unproven statement based on observations

• A logical fallacy

• A mathematical theorem

What is a counterexample?

• An example that supports a conjecture

• An example that disproves a conjecture

• A proven theorem

• A logical argument

In the example given, what happens at each position in the sequence of shapes?

• A box is colored

• A box is rotated

• A box is added

• A box is removed

Which of the following sums is a counterexample to the conjecture 'the sum of two numbers is always greater than the greatest number'?

• 12 + 10

• 2 + 6

• 5 + 3

• −5 + 2

What does the law of detachment state?

• If a statement is true, its converse is also true

• If a statement is true, then a related statement is also true

• If two segments are equal, they are congruent

• If a statement is true, then its negation is false

In the law of detachment example, what is the relationship between segment AB and segment CD?

• They are similar

• They are perpendicular

• They are congruent

• They are parallel

What does the law of syllogism allow you to do?

• Combine two statements to form a third statement

• Prove a statement by contradiction

• Find the converse of a statement

• Disprove a statement using a counterexample

In the law of syllogism example, what can be concluded if x > 5?

• x^2 < 20

• x^2 > 20

• x^2 < 25

• x^2 > 25

Which law is used when you derive a new statement from two given statements?

• Law of Detachment

• Law of Syllogism

• Law of Contradiction

• Law of Excluded Middle

What is the main focus of Chapter 2 Section 2 in Geometry?

• Trigonometric identities

• Triangles and their properties

• Inductive and deductive reasoning

• Coordinate geometry