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

Grade 10 Math Worksheet

Circle the best answer.

1. 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 not a multiple of 9, then it is not a multiple of 3.
   • If a number is a multiple of 3, then it is 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 a multiple of 3, then it is not a multiple of 9.
2. 2.

   "If a number is a multiple of 12, then it is a multiple of 6." Bo teaches a rule to a number-sorting robot. Which statement is the converse of the rule?

   • If a number is a multiple of 6, then it is a multiple of 12.
   • If a number is not a multiple of 6, then it is not a multiple of 12.
   • If a number is a multiple of 6, then it is not a multiple of 12.
   • If a number is not a multiple of 12, then it is not a multiple of 6.
3. 3.

   "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 not greater than 12, then it is not 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 greater than 12, then it is greater than 20.
4. 4.

   "If an angle measures 150°, then it is obtuse." Milo cuts out a rule card. Which statement is the contrapositive of the rule?

   • If an angle is obtuse, then it measures 150°.
   • If an angle is obtuse, then it does not measure 150°.
   • If an angle is not obtuse, then it does not measure 150°.
   • If an angle does not measure 150°, then it is not obtuse.
5. 5.

   "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 is not a hexagon, then it does not have more than four sides.
   • If a polygon has more than four sides, then it is not a hexagon.
   • If a polygon has more than four sides, then it is a hexagon.
6. 6.

   "If 2x = 14, then x = 7." Zee finds a rule in a puzzle book. Which statement is the inverse of the rule?

   • If x ≠ 7, then 2x ≠ 14.
   • If 2x ≠ 14, then x ≠ 7.
   • If x = 7, then 2x ≠ 14.
   • If x = 7, then 2x = 14.
7. 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?

   • 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°.
   • Yes: the converse of a true rule is always true.
8. 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?

   • No: a triangle is not a pentagon and has only three sides.
   • Yes: a pentagon has five sides, more than three.
   • Yes: the converse of a true rule is always true.
   • No: a square has more than three sides but is not a pentagon.
9. 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?

   • Yes: the converse of a true rule is always 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.
10. 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.