Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram

Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram

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"Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram? a. Two pairs of sides are parallel. b. Two pairs of opposite sides are congruent. c. Two angles are supplementary. d. Two diagonals bisect each other."

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ANSWER:

C. Two angles are supplementary

A. B. D. are proven that a quadrilateral is a parallelogram.

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There are five ways in which you can prove that a quadrilateral is a parallelogram. The first four are the converses of parallelogram properties (including the definition of a parallelogram). Make sure you remember the oddball fifth one — which isn’t the converse of a property — because it often comes in handy:
  • If both pairs of opposite sides of a quadrilateral are parallel, then it’s a parallelogram (reverse of the definition).

  • If both pairs of opposite sides of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).

    Tip:To get a feel for why this proof method works, take two toothpicks and two pens or pencils of the same length and put them all together tip-to-tip; create a closed figure, with the toothpicks opposite each other. The only shape you can make is a parallelogram.

  • If both pairs of opposite angles of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).

  • If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram (converse of a property).

    Tip: Take, say, a pencil and a toothpick (or two pens or pencils of different lengths) and make them cross each other at their midpoints. No matter how you change the angle they make, their tips form a parallelogram.

  • If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram (neither the reverse of the definition nor the converse of a property).

    Tip: Take two pens or pencils of the same length, holding one in each hand. If you keep them parallel, no matter how you move them around, you can see that their four ends form a parallelogram.

The preceding list contains the converses of four of the five parallelogram properties. If you’re wondering why the converse of the fifth property (consecutive angles are supplementary) isn’t on the list, you have a good mind for details. The explanation, essentially, is that the converse of this property, while true, is difficult to use, and you can always use one of the other methods instead.

About This Article

This article is from the book:

  • Geometry For Dummies ,

About the book author:

Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

This article can be found in the category:

  • Geometry ,

Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram

Transcribed Image Text:3. Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram? A. Two pairs of sides are parallel. B. Two pairs of opposite sides are congruent. C. Two angles are supplementary. D. Two diagonals bisect each other. 4. What is true about the diagonals of a parallelogram? A. They are always congruent. B. They are always perpendicular. C. They always bisect each other. D. They always form four congruent angles. 5. Which of these statements is not true about parallelograms? A. Parallelograms are always quadrilateral. B. Opposite angles of a parallelogram are always supplementary. C. Diagonals of a parallelogram always intersect at a point. D. Opposite sides of a parallelogram are always parallel.

Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram

Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram

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Which of the following conditions is sufficient to prove that a quadrilateral is a parallelogram?

To prove a quadrilateral is a parallelogram, you must use one of these five ways. Prove that both pairs of opposite sides are parallel. Prove that both pairs of opposite sides are congruent. Prove that one pair of opposite sides is both congruent and parallel.

Which of the following is not a condition that a quadrilateral is a parallelogram?

Answer and Explanation: Indicating that the two opposite sides are parallel is not a sure indicator of a parallelogram because a trapezoid has two opposite sides that are parallel but the remaining opposite sides are not.

What are the 4 conditions for a given quadrilateral to be a parallelogram?

Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. The diagonals bisect each other. One angle is supplementary to both its consecutive angles.