Geometry Unit 2

Which of the following statements best illustrates the concept of inductive reasoning?

• Every time I see a swan, it is white, so all swans must be white.
• If it is a square, then it is a rectangle.
• The sum of the angles in a triangle is always 180 degrees.
• If two angles are congruent, then they are equal.

What is the primary purpose of inductive reasoning?

• To form a conclusion based on specific examples.
• To prove a statement using deductive logic.
• To analyze the validity of a conjecture.
• To establish a universal truth.

Which of the following is an example of inductive reasoning?

• All observed swans are white, so all swans must be white.
• If it rains, then the ground is wet.
• The sum of angles in a triangle is always 180 degrees.
• If two angles are congruent, then they are equal.

Which of the following best describes a conjecture?

• A statement that is always true.
• An educated guess based on known information.
• A logical argument that uses deductive reasoning.
• A definitive proof of a mathematical statement.

If the sequence is 2, 4, 8, 16, what would be a reasonable conjecture for the next number?

• 20
• 64
• 24
• 32

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

If a conjecture states that 'All swans are white', what would be a suitable counterexample?

• A black swan.
• A white swan.
• A swan in a zoo.
• A picture of a swan.

What is a counterexample used for in mathematics?

• To create a new conjecture.
• To show that a given statement is not always true.
• To prove a statement is always true.
• To summarize a mathematical argument.

Which of the following is a valid counterexample to the conjecture 'If AB = BC, then B is the midpoint of AC'?

• A diagram where AC is equal to AB.
• A diagram where AB is greater than BC.
• A diagram where B is outside of segment AC.
• A diagram where B is between A and C.

Tags

CCSS.HSG.CO.A.1

In the conditional statement 'If it rains, then the ground is wet', what is the hypothesis?

• The ground is wet.
• It rains.
• If it rains.
• Then the ground is wet.

What does the conclusion represent in a conditional statement?

• The condition that must be met.
• The outcome that follows the hypothesis.
• The negation of the hypothesis.
• The entire statement.