Question

1. if you eat breakfast, then you won’t be hungry in the morning.

• converse: ____
• true/false? ____
• counterexample: ____

2-4
classwork
page 2
if-then statements and counterexamples
geometry
olympia hs
2025-26
directions: for each statement, underline the hypothesis (after if), box the conclusion (after then), write the converse, and decide if the converse is true or false. if it is false, provide a counterexample. at the end, create your own statements.

1. if a number is even, then it is divisible by 2.

• converse: ____
• true/false? ____
• counterexample: ____

1. if a number ends in 5, then it is divisible by 5.

• converse: ____
• true/false? ____
• counterexample: ____

1. if a shape has 3 sides, then it is a triangle.

• converse: ____
• true/false? ____
• counterexample: ____

1. if a polygon is a pentagon, then it has 5 sides.

• converse: ____
• true/false? ____
• counterexample: ____

1. write your own conditional statement about school. underline the hypothesis and put a box around the conclusion.
2. swap with a partner and try to find a counterexample for their statement.

• converse: ____
• true/false? ____
• counterexample: ____

Explanation:

Problem 1:

Step1: Identify hypothesis and conclusion

Hypothesis: \underline{a number is even}, Conclusion: \boxed{it is divisible by 2}

Step2: Write the converse

Converse: If a number is divisible by 2, then it is even.

Step3: Determine True/False

A number divisible by 2 has a factor of 2, so it's even. So True.

Step4: Counterexample (not needed as it's true)

None.

Step1: Identify hypothesis and conclusion

Hypothesis: \underline{a number ends in 5}, Conclusion: \boxed{it is divisible by 5}

Step2: Write the converse

Converse: If a number is divisible by 5, then it ends in 5.

Step3: Determine True/False

Numbers like 10 are divisible by 5 but end in 0, so False.

Step4: Counterexample

10 is divisible by 5 (10 ÷ 5 = 2) but does not end in 5.

Step1: Identify hypothesis and conclusion

Hypothesis: \underline{a shape has 3 sides}, Conclusion: \boxed{it is a triangle}

Step2: Write the converse

Converse: If a shape is a triangle, then it has 3 sides.

Step3: Determine True/False

By definition, a triangle has 3 sides. So True.

Step4: Counterexample (not needed as it's true)

None.

Answer:

• Converse: If a number is divisible by 2, then it is even.
• True/False? True
• Counterexample: None

Problem 2: