Convert the following statement into an If-Then form: All Floridians have been to the beach. Write your answer in the If-Then column.

If a person is a Floridian, then they have been to the beach.

If a person has been to the beach, then they are a Floridian.

If a person is not a Floridian, then they have not been to the beach.

If a person has not been to the beach, then they are not a Floridian.

Convert the following statement into a biconditional statement: The four angles at the point of intersection of two lines are right angles if the intersecting lines are perpendicular.

The four angles at the point of intersect of two lines are right angles if and only if the lines are perpendicular.

If two lines are parallel, then all four angles at the point of intersection are right angles.

If two lines intersect, then only two angles at the point of intersection are right angles.

If two lines intersect, then all four angles at the point of intersection are acute angles.

For the conditional statement: If Anthony has visited the Southernmost Point Buoy, then he has been to Key West. Identify the Hypothesis and Conclusion.

Hypothesis: Anthony has visited the Southernmost Point Buoy. Conclusion: He has been to Key West.

Hypothesis: He has been to Key West. Conclusion: Anthony has visited the Southernmost Point Buoy.

Hypothesis: Anthony has visited the Southernmost Point Buoy. Conclusion: He has not been to Key West.

Hypothesis: Anthony has not visited the Southernmost Point Buoy. Conclusion: He has been to Key West.

Write the following conditional using 'if and only if.' If the sum of two angles is 180°, then the angles are supplementary. Write your answer in the Biconditional box.

Two angles are supplementary if and only if the sum of their measures is 180°.

Two angles are supplementary if and only if the sum of their measures is 90°.

Two angles are supplementary if and only if they are both right angles.

Two angles are supplementary if and only if their difference is 180°.

An incomplete proof is shown. Complete the reasons for steps 2, 3, & 4. Given: m∠MKB + m∠BKN = 90° Prove: m∠RKD + m∠BKN = 90°

2. Vertical Angles Theorem 3. Definition of Congruent Angles 4. Substitution

2. Corresponding Angles Postulate 3. Addition Property of Equality 4. Reflexive Property

2. Alternate Interior Angles Theorem 3. Subtraction Property of Equality 4. Transitive Property

2. Angle Bisector Theorem 3. Definition of Supplementary Angles 4. Division Property of Equality

For the conditional statement: If m∠MKN = 90°, then m∠MKB + m∠BKN = 90°. Identify the converse of the statement.

If m∠MKB + m∠BKN = 90°, then m∠MKN = 90°.

If m∠MKN = 90°, then m∠MKB = m∠BKN.

If m∠MKB + m∠BKN = 180°, then m∠MKN = 90°.

If m∠MKN = 90°, then m∠MKB + m∠BKN = 180°.

Identify the Inverse relationship to conditional.

If m∠MKN ≠ 90°, then m∠MKB + m∠BKN ≠ 90°.

If m∠MKN = 90°, then m∠MKB + m∠BKN ≠ 90°.

If m∠MKN ≠ 90°, then m∠MKB + m∠BKN = 90°.

If m∠MKN = 90°, then m∠MKB + m∠BKN = 90°.

For the conditional statement: If m∠MKN = 90°, then m∠MKB + m∠BKN = 90°. Identify the Contrapositive relationship to conditional.

If m∠MKB + m∠BKN ≠ 90°, then m∠MKN ≠ 90°.

If m∠MKN ≠ 90°, then m∠MKB + m∠BKN ≠ 90°.

If m∠MKB + m∠BKN = 90°, then m∠MKN = 90°.

If m∠MKN = 90°, then m∠MKB + m∠BKN ≠ 90°.

A conditional statement is biconditional if and only if both the statement and its converse are true. Which of the following best explains why a conditional statement is biconditional?

Because both the statement and its converse are true

Because only the statement is true

Because only the converse is true

Because neither the statement nor its converse is true

A series of steps is possible in the game of UNO. Each statement represents a card played. Without using a wild card, add a fifth statement and provide the reason for the series of steps. Previous steps: 1. Blue 5 (Given), 2. Blue 2 (Matches color), 3. Yellow 2 (Matches number), 4. Yellow 7 (Matches color). Statement 5: ______. Reason 5: ______.

Statement 5: Red 7. Reason 5: Matches number.

Statement 5: Blue 7. Reason 5: Matches color.

Statement 5: Yellow 5. Reason 5: Matches number.

Statement 5: Green 2. Reason 5: Matches number.

How can you prove step #5?

Transitive property of congruence

Subtraction property of equality

Definition of supplementary angles

Proofs and Logic Practice_9/10/25

Authored by Tiffany Wallace-Coleman

Mathematics

10th Grade

20 Questions

CCSS covered

Used 3+ times

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

Determine the type of reasoning for the following statement: Sofia notices that the dogs on her street bark at a delivery truck, so Sofia concludes that all dogs bark at delivery trucks.

Inductive reasoning

Deductive reasoning

Analogical reasoning

Abductive reasoning

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Determine the type of reasoning for the following statement: Florida requires all lawyers to pass the bar exam to practice. If Mark does not pass the bar, then he will not legally be able to represent as their lawyer.

Deductive reasoning

Inductive reasoning

Analogical reasoning

Abductive reasoning

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

MULTIPLE CHOICE QUESTION

1 min • 1 pt

An incomplete proof is shown. Complete the reason for step 2.

Definition of congruent angles

Addition Property of Equality

Vertical Angles Theorem

Transitive Property of Equality

Tags

CCSS.HSG.SRT.B.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which step contains the error? Error Step______

Step 3

Step 1

Step 2

Step 4

Tags

CCSS.6.EE.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What card, other than a wild card, would correctly complete the steps? Card ______

Red 3

Blue 5

Yellow 7

Green 2

Tags

CCSS.6.EE.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A statement is shown. “If it is my birthday, then I will eat ice cream.” a. Write the converse of the statement. Converse ______

If I eat ice cream, then it is my birthday.

If it is not my birthday, then I will not eat ice cream.

If I do not eat ice cream, then it is not my birthday.

If it is my birthday, then I will not eat ice cream.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A statement is shown. “If it is my birthday, then I will eat ice cream.” b. Write a counterexample that shows the converse is not true. Counterexample ______

I ate ice cream, but it was not my birthday.

It was my birthday, and I ate cake.

I did not eat ice cream, and it was not my birthday.

I ate ice cream on my birthday.

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

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