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 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 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 not greater than 20.
2. 2.

   "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 has four sides, then it is a rectangle.
   • If a shape has 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 does not have four sides, then it is not a rectangle.
3. 3.

   "If a number is a multiple of 8, then it is a multiple of 4." Kira writes a rule card in pencil. Which statement is the contrapositive of the rule?

   • If a number is a multiple of 4, then it is not a multiple of 8.
   • If a number is a multiple of 4, then it is a multiple of 8.
   • If a number is not a multiple of 4, then it is not a multiple of 8.
   • If a number is not a multiple of 8, then it is not a multiple of 4.
4. 4.

   "If a number is a multiple of 20, then it ends in 0." Luz reads a rule card while the clock ticks. Which statement is the contrapositive of the rule?

   • If a number ends in 0, then it is a multiple of 20.
   • If a number ends in 0, then it is not a multiple of 20.
   • If a number is not a multiple of 20, then it does not end in 0.
   • If a number does not end in 0, then it is not a multiple of 20.
5. 5.

   "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 50, then it is not greater than 30.
   • 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 not greater than 50.
   • If a number is greater than 30, then it is greater than 50.
6. 6.

   "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 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.
   • If a number is a multiple of 5, then it is a multiple of 15.
   • If a number is not a multiple of 15, then it is not a multiple of 5.
7. 7.

   "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 has more than four sides, then it is not a hexagon.
   • 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 is not a hexagon, then it does not have more than four sides.
8. 8.

   "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 x = 7, then 2x = 14.
   • If x ≠ 7, then 2x ≠ 14.
   • If 2x ≠ 14, then x ≠ 7.
9. 9.

   "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: 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.
   • No: a triangle is not a pentagon and has only three sides.
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: a 45° angle is not a right angle.
    • Yes: a 90° angle is a right angle.
    • No: the converse of a rule is never true.