Which statements prove that a quadrilateral is a parallelogram?

Select each correct answer.

Quadrilateral DEFG has one diagonal that bisects the other diagonal.

Quadrilateral DEFG has only one set of opposite angles that are congruent.

Quadrilateral DEFG has two sets of consecutive angles that are supplementary.

Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.

Question

09-10-2017
Mathematics

contestada

Which statements prove that a quadrilateral is a parallelogram?

Select each correct answer.

Quadrilateral DEFG has one diagonal that bisects the other diagonal.

Quadrilateral DEFG has only one set of opposite angles that are congruent.

Quadrilateral DEFG has two sets of consecutive angles that are supplementary.

Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.

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Nadeshiko Nadeshiko · Answer 1 · 2017-10-09T19:01:51+02:00

First, let's list the properties of parallelograms. *Opposite sides are congruent
*Opposite angles are congruent
*Consecutive angles are supplementary
*The diagonals of a parallelogram bisect each other.

Statement 1: This statement does not prove that the quadrilateral is a parallelogram because both diagonals have to bisect each other and not only one.

Statement 2: A parallelogram has two sets of opposite angles not only one. The statement would prove the quadrilateral is a parallelogram if it said that the quadrilateral has two sets of opposite angles that are congruent.

Statement 3: This statement is a property of a parallelogram. However, it doesn't prove that a quadrilateral is a parallelogram.

Statement 4: This statement proves that the quadrilateral is a parallelogram. If the statement, however, said that the quadrilateral has one set of opposite sides that are only congruent or only parallel, then it would not prove the quadrilateral to be a parallelogram.

ahirohit963 ahirohit963 · Answer 2 · 2021-11-09T11:30:30+01:00

The statement "Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel" proves that a quadrilateral is a parallelogram.

A quadrilateral has 4 sides and the sum of interior angles are [tex]360^\circ[/tex] where as the parallelogram is a quadrilateral whose oppposite sides are parallel to each other.

The following statements are:

A). The statement "Quadrilateral DEFG has one diagonal that bisects the other diagonal" is incorrect because both diagonals have to bisect each other.

B). The statement "Quadrilateral DEFG has only one set of opposite angles that are congruent" is incorrect because a quadrilateral is a parallelogram when it has two sets of opposite angles that are congruent.

C). The statement "Quadrilateral DEFG has two sets of consecutive angles that are supplementary" is incorrect although it is a property of parallelogram.

D). The statement "Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel" is correct this statement proves that a quadrilateral is a parallelogram.

For more information, refer the link given below:

https://brainly.com/question/22642276