Question

underline the hypothesis and circle the conclusion of each conditional statement. then write the converse, biconditional (if possible), inverse and contrapositive statements.

1. if three points are not on the same line, then they are non - collinear.

converse
biconditional
inverse
contrapositive

1. if two angles are right angles, then they are congruent.

converse
biconditional
inverse
contrapositive

1. if it is a fish, then it lives in water.

converse
biconditional
inverse
contrapositive

Explanation:

1. For the statement "If two angles are right angles, then they are congruent":

• Hypothesis: Two angles are right angles.
• Conclusion: They are congruent.
• Converse: If two angles are congruent, then they are right - angles.
• Biconditional: Not possible as just because angles are congruent doesn't mean they are right - angles and vice - versa.
• Inverse: If two angles are not right angles, then they are not congruent.
• Contrapositive: If two angles are not congruent, then they are not right angles.

1. For the statement "If it is a fish, then it lives in water":

• Hypothesis: It is a fish.
• Conclusion: It lives in water.
• Converse: If it lives in water, then it is a fish.
• Biconditional: Not possible as there are other water - living creatures besides fish.
• Inverse: If it is not a fish, then it does not live in water.
• Contrapositive: If it does not live in water, then it is not a fish.

Answer:

1.

• Hypothesis: Underline "Two angles are right angles"
• Conclusion: Circle "they are congruent"
• Converse: If two angles are congruent, then they are right angles.
• Biconditional: Not possible
• Inverse: If two angles are not right angles, then they are not congruent.
• Contrapositive: If two angles are not congruent, then they are not right angles.

2.

• Hypothesis: Underline "It is a fish"
• Conclusion: Circle "it lives in water"
• Converse: If it lives in water, then it is a fish.
• Biconditional: Not possible
• Inverse: If it is not a fish, then it does not live in water.
• Contrapositive: If it does not live in water, then it is not a fish.