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State the converses of the following statements. In each case, also decide whether the converse is true or false.
(1) If n is an even integer, then 2n + 1 is an odd integer.
(2) If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
(3) If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.
(4) If the decimal expansion of a real number is terminating, then the number is rational.

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Answer:

See below.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

  • Hypothesis:  The part after the "if".
  • Conclusion:  The part after the "then".

Question 1

Given statement:  If n is an even integer, then 2n + 1 is an odd integer.

  • Hypothesis: "n is an even integer"
  • Conclusion:  "2n + 1 is an odd integer"

Converse:  If 2n + 1 is an odd integer, then n is an even integer.

Question 2

Given statement:  If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

  • Hypothesis: "a transversal intersects two parallel lines"
  • Conclusion: "each pair of corresponding angles is equal"

Converse:  If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.

Question 3

Given statement:  If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.

  • Hypothesis: "each pair of opposite sides of a quadrilateral is equal"
  • Conclusion: "the quadrilateral is a parallelogram"

Converse:  If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.

Question 4

Given statement:  If the decimal expansion of a real number is terminating, then the number is rational.

  • Hypothesis: "the decimal expansion of a real number is terminating"
  • Conclusion: "the number is rational"

Converse:  If a real number is rational, then the decimal expansion of the number is terminating.

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