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

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Bo writes a rule with a freshly sharpened pencil: "If a shape is a square, then it has four sides." Which part is the hypothesis (the part right after "if")?

   • it has four sides
   • a shape is not a square
   • a shape is a square
2. 2.

   Esme writes a rule in a puzzle book: "If an angle measures 30°, then it is acute." Which part is the conclusion (the part right after "then")?

   • it is acute
   • an angle measures 30°
   • it is not acute
3. 3.

   Jun writes a rule in a math notebook: "If a number is greater than 10, then it is greater than 5." Which part is the hypothesis (the part right after "if")?

   • a number is greater than 10
   • it is greater than 5
   • a number is not greater than 10

4. Read this first

   Rule

   "If a number is a multiple of 6, then it is a multiple of 3." New statement: "If a number is not a multiple of 3, then it is not a multiple of 6."

5. 4.

   Kira rewrites a rule on a sheet of paper. The parts are P: "a number is a multiple of 6" and Q: "it is a multiple of 3". What is the new statement called?

   • the inverse
   • the contrapositive
   • the same rule
   • the converse

6. Rule

   "If an angle measures 120°, then it is obtuse." New statement: "If an angle is not obtuse, then it does not measure 120°."

7. 5.

   Luz rewrites a rule in big crayon letters. The parts are P: "an angle measures 120°" and Q: "it is obtuse". What is the new statement called?

   • the converse
   • the same rule
   • the inverse
   • the contrapositive

8. Rule

   "If a number is a multiple of 4, then it is even." New statement: "If a number is even, then it is a multiple of 4."

9. 6.

   Milo rewrites a rule for a number-sorting robot. The parts are P: "a number is a multiple of 4" and Q: "it is even". What is the new statement called?

   • the contrapositive
   • the inverse
   • the converse
   • the same rule

10. Rule

    "If a solid is a cube, then it has six faces." New statement: "If a solid is not a cube, then it does not have six faces."

11. 7.

    Noah rewrites a rule on a cardboard box. The parts are P: "a solid is a cube" and Q: "it has six faces". What is the new statement called?

    • the contrapositive
    • the converse
    • the inverse
    • the same rule
12. 8.

    Pia draws two circles on graph paper. Which if-then rule does the picture show?

    • If a number is a multiple of 5, then it is a multiple of 10.
    • If a number is a multiple of 5, then it is not a multiple of 10.
    • If a number is a multiple of 10, then it is a multiple of 5.
13. 9.

    Ren draws two circles with a pencil. Which if-then rule does the picture show?

    • If a whole number is odd, then it ends in 5.
    • If a whole number is odd, then it does not end in 5.
    • If a whole number ends in 5, then it is odd.
14. 10.

    Tala draws two circles on a card. Which if-then rule does the picture show?

    • If an angle measures 45°, then it is acute.
    • If an angle is acute, then it does not measure 45°.
    • If an angle is acute, then it measures 45°.