Question

Which statements prove that a quadrilateral is a parallelogram?

Answer 1

Answer:

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.      

Answer 2

Answer:

a.Quadrilateral DEFG has opposite angles that are congruent then it is a parallelogram.

b.Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.Then , it is parallelogram.

Step-by-step explanation:

We have to find the statement which prove that a quadrilateral is a parallelogram.

We know that property of parallelogram

1.Opposite sides are congruent and parallel.

2.Opposite angles are congruent.

3.Sum of consecutive angles are supplementary.

4.Diagonals of parallelogram bisect to each other.

a.Quadrilateral DEFG has opposite angles that are congruent then it is a parallelogram.

It is true.

b.Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.Then , it is parallelogram.

It is true.

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

It is false because sum of consecutive angles are supplemenatry.

d.Quadrilateral DEFG has diagonals that are congruent .

It is not true because it is not necessary but the diagonals of parallelogram bisect to each other.