Worksheets · Geometry

Conditional statements worksheet

An if-then statement has a hypothesis (after "if") and a conclusion (after "then"). Swap them for the converse. Negate both for the inverse. Swap and negate for the contrapositive, which always has the same truth value as the original; the other two need not. Some questions ask whether a converse is true, or what you can conclude from two statements by detachment or syllogism.

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Name

Conditional Statements

Date Period

Write what is asked.

  1. Write the converse, inverse or contrapositive

    Write the converse of: If two angles are vertical, then they are congruent.
  2. Write the converse of: If an animal is a dog, then it is a mammal.
  3. Write the contrapositive of: If a quadrilateral is a rhombus, then its four sides are congruent.
  4. Write the inverse of: If an animal is a dog, then it is a mammal.
  5. Write the converse of: If an angle is acute, then it measures less than 90°.

  1. Identify the hypothesis and conclusion

    Identify the hypothesis and conclusion: If a number is divisible by 6, then it is divisible by 3.
  2. Identify the hypothesis and conclusion: It has four equal sides if a shape is a square.
  3. Identify the hypothesis and conclusion: If it is raining, then the ground is wet.
  4. Identify the hypothesis and conclusion: You live in the United States if you live in Texas.
  5. Identify the hypothesis and conclusion: If a polygon is a triangle, then its angles add to 180°.

  1. Write the converse and test it

    Write the converse of: If x=−6, then x3=−216. Is the converse true? If not, give a counterexample.
  2. Write the converse of: If x=−2, then x2=4. Is the converse true? If not, give a counterexample.
  3. Write the converse of: If x=−7, then 2x+5=−9. Is the converse true? If not, give a counterexample.
  4. Write the converse of: If x=6, then x2=36. Is the converse true? If not, give a counterexample.
  5. Write the converse of: If x=9, then 2x+8=26. Is the converse true? If not, give a counterexample.

  1. Draw a conclusion from the statements

    If the battery dies, then the phone turns off. The battery dies. What can you conclude?
  2. If the alarm rings, then Maya wakes up. The alarm rings. What can you conclude?
  3. If ABCD is a square, then ABCD is a rectangle. ABCD is a rectangle. What can you conclude?
  4. If it rains, then the game is canceled. If the game is canceled, then we go home early. What can you conclude?
  5. If ABCD is a square, then ABCD is a rectangle. ABCD is a square. What can you conclude?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Conditional StatementsAnswer keyVersion 1

Date Period

Write what is asked.

  1. Write the converse, inverse or contrapositive

    Write the converse of: If two angles are vertical, then they are congruent.If they are congruent, then two angles are vertical.
  2. Write the converse of: If an animal is a dog, then it is a mammal.If it is a mammal, then an animal is a dog.
  3. Write the contrapositive of: If a quadrilateral is a rhombus, then its four sides are congruent.If its four sides are not congruent, then a quadrilateral is not a rhombus.
  4. Write the inverse of: If an animal is a dog, then it is a mammal.If an animal is not a dog, then it is not a mammal.
  5. Write the converse of: If an angle is acute, then it measures less than 90°.If it measures less than 90°, then an angle is acute.

  1. Identify the hypothesis and conclusion

    Identify the hypothesis and conclusion: If a number is divisible by 6, then it is divisible by 3.H: a number is divisible by 6; C: it is divisible by 3
  2. Identify the hypothesis and conclusion: It has four equal sides if a shape is a square.H: a shape is a square; C: it has four equal sides
  3. Identify the hypothesis and conclusion: If it is raining, then the ground is wet.H: it is raining; C: the ground is wet
  4. Identify the hypothesis and conclusion: You live in the United States if you live in Texas.H: you live in Texas; C: you live in the United States
  5. Identify the hypothesis and conclusion: If a polygon is a triangle, then its angles add to 180°.H: a polygon is a triangle; C: its angles add to 180°

  1. Write the converse and test it

    Write the converse of: If x=−6, then x3=−216. Is the converse true? If not, give a counterexample.If x3=−216, then x=−6. True
  2. Write the converse of: If x=−2, then x2=4. Is the converse true? If not, give a counterexample.If x2=4, then x=−2. False: x=2
  3. Write the converse of: If x=−7, then 2x+5=−9. Is the converse true? If not, give a counterexample.If 2x+5=−9, then x=−7. True
  4. Write the converse of: If x=6, then x2=36. Is the converse true? If not, give a counterexample.If x2=36, then x=6. False: x=−6
  5. Write the converse of: If x=9, then 2x+8=26. Is the converse true? If not, give a counterexample.If 2x+8=26, then x=9. True

  1. Draw a conclusion from the statements

    If the battery dies, then the phone turns off. The battery dies. What can you conclude?The phone turns off.
  2. If the alarm rings, then Maya wakes up. The alarm rings. What can you conclude?Maya wakes up.
  3. If ABCD is a square, then ABCD is a rectangle. ABCD is a rectangle. What can you conclude?No conclusion
  4. If it rains, then the game is canceled. If the game is canceled, then we go home early. What can you conclude?If it rains, then we go home early.
  5. If ABCD is a square, then ABCD is a rectangle. ABCD is a square. What can you conclude?ABCD is a rectangle.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Write the contrapositive of: If a shape is a square, then it has four equal sides.

  1. Swap the two parts, and negate each.
  2. Not four equal sides, so not a square.

The answer is If a shape does not have four equal sides, then it is not a square..

Where students go wrong

Mixing up converse and inverse. Converse swaps, inverse negates; the contrapositive does both.

Also called converse inverse contrapositive, if-then statements, hypothesis and conclusion or logic in geometry.

What you can put on this worksheet

Converse, inverse, contrapositive
Write the converse of: If a number is divisible by 6, then it is divisible by 3. → If it is divisible by 3, then a number is divisible by 6.
Hypothesis and conclusion
Identify the hypothesis and conclusion: If a number is divisible by 6, then it is divisible by 3. → H: a number is divisible by 6; C: it is divisible by 3
Is the converse true?
Write the converse of: If x=7, then 2x+1=15. Is the converse true? If not, give a counterexample. → If 2x+1=15, then x=7. True
Detachment and syllogism
If angles 1 and 2 are vertical angles, then angles 1 and 2 are congruent. If angles 1 and 2 are congruent, then angles 1 and 2 have equal measures. What can you conclude? → If angles 1 and 2 are vertical angles, then angles 1 and 2 have equal measures.

Questions about these worksheets

Yes. Every conditional statements sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the conditional statements questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: converse, inverse, contrapositive, hypothesis and conclusion, is the converse true? and detachment and syllogism. Tick as many as you want and set how many of each, or let it spread them evenly.

Mixing up converse and inverse. Converse swaps, inverse negates; the contrapositive does both.