Question

Which statements prove that a quadrilateral is a parallelogram?

Select each correct answer (more than one answer)


Quadrilateral DEFG has opposite angles that are congruent.

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

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

Quadrilateral DEFG has diagonals that are congruent.

Answer 1

A quadrilateral is a parallelogram if it satisfies certain conditions, such as having congruent opposite angles, congruent and parallel opposite sides, and congruent diagonals.

Step-by-step explanation:

A quadrilateral is a parallelogram if it satisfies certain conditions. The statements that prove a quadrilateral is a parallelogram are:

1. Quadrilateral DEFG has opposite angles that are congruent: If the opposite angles in a quadrilateral are congruent, then it is a parallelogram.
2. Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel: If one pair of opposite sides in a quadrilateral are both congruent and parallel, then it is a parallelogram.
3. Quadrilateral DEFG has diagonals that are congruent: If the diagonals in a quadrilateral are congruent, then it is a parallelogram.

Answer 2

1st and 2nd statements are true.

Step-by-step explanation:

We are asked to choose the correct statements that can prove that quadrilateral DEFG is a parallelogram.

We will use parallelogram properties to answer this problem.

Since we know that a parallelogram has two sets of opposite angles congruent, therefore, 1st option is a correct choice.

Since a parallelogram has one set of opposite sides that are both congruent and parallel, therefore, second statement is true.

Since the consecutive angles of a parallelogram are supplementary, therefore, 3rd statement is not true.

Since the diagonals of parallelogram bisect each other, therefore, 4th statement is not true.