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10th grade If-then statements: converse, inverse, contrapositive and "if and only if" worksheet

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If-then statements: converse, inverse, contrapositive and "if and only if"

Grade 10 Math Worksheet

NameDate

Circle the best answer.

  1. "If a number is a multiple of 9, then it is a multiple of 3." Ari copies a rule card into a notebook. Which statement is the converse of the rule?

    • If a number is a multiple of 3, then it is a multiple of 9.
    • If a number is a multiple of 3, then it is not a multiple of 9.
    • If a number is not a multiple of 3, then it is not a multiple of 9.
    • If a number is not a multiple of 9, then it is not a multiple of 3.

  2. "If a number is greater than 20, then it is greater than 12." Esme finds a rule in a puzzle book. Which statement is the converse of the rule?

    • If a number is greater than 12, then it is greater than 20.
    • If a number is greater than 12, then it is not greater than 20.
    • If a number is not greater than 20, then it is not greater than 12.
    • If a number is not greater than 12, then it is not greater than 20.

  3. "If a shape is a rectangle, then it has four sides." Jun tapes a rule card to the classroom window. Which statement is the converse of the rule?

    • If a shape does not have four sides, then it is not a rectangle.
    • If a shape is not a rectangle, then it does not have four sides.
    • If a shape has four sides, then it is a rectangle.
    • If a shape has four sides, then it is not a rectangle.

  4. "If a number is greater than 50, then it is greater than 30." Pia copies a rule card into a notebook. Which statement is the inverse of the rule?

    • If a number is not greater than 30, then it is not greater than 50.
    • If a number is greater than 30, then it is greater than 50.
    • If a number is greater than 30, then it is not greater than 50.
    • If a number is not greater than 50, then it is not greater than 30.

  5. "If a number is a multiple of 15, then it is a multiple of 5." Ren teaches a rule to a number-sorting robot. Which statement is the inverse of the rule?

    • If a number is not a multiple of 15, then it is not a multiple of 5.
    • If a number is a multiple of 5, then it is a multiple of 15.
    • If a number is not a multiple of 5, then it is not a multiple of 15.
    • If a number is a multiple of 5, then it is not a multiple of 15.

  6. "If a polygon is a hexagon, then it has more than four sides." Tala draws a rule card on the back of a map. Which statement is the inverse of the rule?

    • If a polygon does not have more than four sides, then it is not a hexagon.
    • If a polygon has more than four sides, then it is a hexagon.
    • If a polygon has more than four sides, then it is not a hexagon.
    • If a polygon is not a hexagon, then it does not have more than four sides.

  7. "If an angle measures 20°, then it is acute." Ari checks a rule card for the math club. The converse is "If an angle is acute, then it measures 20°." Is the converse true?

    • Yes: the converse of a true rule is always true.
    • No: a 70° angle is acute but does not measure 20°.
    • No: a 130° angle is not acute and does not measure 20°.
    • Yes: a 20° angle is acute and measures 20°.

  8. "If a polygon is a pentagon, then it has more than three sides." Bo checks a rule card for the math club. The converse is "If a polygon has more than three sides, then it is a pentagon." Is the converse true?

    • Yes: the converse of a true rule is always true.
    • No: a square has more than three sides but is not a pentagon.
    • No: a triangle is not a pentagon and has only three sides.
    • Yes: a pentagon has five sides, more than three.

  9. "If a number is a multiple of 100, then it is even." Esme checks a rule card for the math club. The converse is "If a number is even, then it is a multiple of 100." Is the converse true?

    • No: 7 is not even and not a multiple of 100.
    • No: 6 is even but not a multiple of 100.
    • Yes: 200 is even and a multiple of 100.
    • Yes: the converse of a true rule is always true.

  10. "If an angle is a right angle, then it measures 90°." Jun checks a rule card for the math club. The converse is "If an angle measures 90°, then it is a right angle." Is the converse true?

    • No: the converse of a rule is never true.
    • No: a 45° angle is not a right angle.
    • Yes: a 90° angle is a right angle.
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10th grade If-then statements: converse, inverse, contrapositive and "if and only if" worksheet – printable
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About this worksheet

If-then statements. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the hypothesis (after "if") and the conclusion (after "then") of a rule.
  • I can write the converse, inverse and contrapositive, and say which one always has the same truth value as the rule.
  • I can tell when a rule works both ways, so it can be written with "if and only if", and read it in symbols.

Standard: no CCSS standard (reasoning language that the proof standards G-CO.C.9–11 rely on)

Words to know

hypothesis: The part of an if-then rule right after "if".

conclusion: The part right after "then".

converse: The rule with its two parts swapped.

inverse: The rule with "not" added to both parts, same order.

contrapositive: Swap the parts and add "not" to both. Always as true as the rule.

counterexample: One case that fits the "if" part but breaks the "then" part.

biconditional: A rule that works both ways, written with "if and only if".

p → q, ~p: "If p, then q" and "not p".

Common mistakes

Your child mixed up the hypothesis (after "if") and the conclusion (after "then").

Your child mixed up the converse (swap the parts) with the contrapositive (swap and add "not"). Try: write one rule four ways and label each.

Your child mixed up the converse (swap the parts) with the inverse (add "not", same order). Try: underline the two parts of a rule, then swap them.

What to say

Ask: which part comes right after the word "if"?

Questions parents ask

What is the most common mistake with if-then statements: converse, inverse, contrapositive and "if and only if"?

Your child mixed up the hypothesis (after "if") and the conclusion (after "then").

How can I help my child with if-then statements: converse, inverse, contrapositive and "if and only if"?

Ask: which part comes right after the word "if"?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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