Proving Quadrilateral

​7.3 Proving that a Quadrilateral Is a Parallelogram

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Multiple Choice

State which method we can use to show that the quadrilateral is a parallelogram. #1

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• Both pairs of diagonals bisect each other.

• Both pairs of opposite sides are parallel.

Multiple Choice

Which is NOT a property of a parallelogram? #2

• Diagonals bisect each other

• Diagonals are congruent

• Both pairs of opposite sides are parallel

• Both pairs of opposite angles are congruent

Multiple Choice

Determine whether the figure is a parallelogram. If so, state the reason. #3

• Yes, quadrilateral with 2 pairs of opposite sides ≅

• Yes, quadrilateral with 2 pairs of opposite angles ≅

• Yes, quadrilateral with diagonals bisecting each other

• not a parallelogram

Multiple Choice

Is this a parallelogram? How do we know? #4

• yes,opposite sides are congruent

• no we can not prove it is a parallelogram

• yes, one pair of sides are congruent and parallel

• yes, opposite sides are parallel

• yes, diagonals bisect each other

Multiple Choice

Is there enough information to determine that this quadrilateral is a parallelogram? #5

• yes

• no

Multiple Choice

Solve for x. #7

• x = 13

• x = 15

• x = 70

• x = 10

Multiple Choice

Is there enough information to determine that this quadrilateral is a parallelogram? #11

• yes

• no

Multiple Choice

Is there enough information to determine that this quadrilateral is a parallelogram? #12

• yes

• no

Multiple Choice

Why is this a parallelogram? #13

• both pairs of opposite angles are congruent

• diagonals bisect each other

• both pairs of opposite sides are congruent

• consecutive angles are supplementary

Multiple Choice

Is there enough information to determine that this quadrilateral is a parallelogram? #15

• yes

• no

Multiple Choice

State which method we can use to show that the quadrilateral is a parallelogram. #17

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• Both pairs of diagonals bisect each other.

• Both pairs of opposite sides are parallel. 

Multiple Choice

Determine the value of x that would classify this quadrilateral as a parallelogram. (The expression are for the tick marks on the diagram). #18

• x = 8

• x = 26

• x = 28

• x = 38

Multiple Choice

How long is the side CD? #19

• 7

• 3

• 35

• 27

Multiple Choice

Find the value of x that makes the quadrilateral a parallelogram. #24

• 5

• 35

• 75

• 55

Multiple Choice

Which theorem can be used to prove the quadrilateral is a parallelogram? #28

• Parallelogram Opposite Sides Converse Theorem

• Parallelogram Opposite Angles Converse Theorem

• Opposite Sides Parallel and Congruent Theorem

• Parallelogram Diagonals Converse Theorem

Multiple Select

For what values of x and y is the polygon a parallelogram? Select all that apply. #29

• y = 43

• y = 26

• x = 19

• x = 10

Multiple Choice

Can you show that this quadrilateral is a parallelogram? #34

• Yes

• No

Multiple Choice

Which theorem shows that the quadrilateral is a parallelogram? #35

• Parallelogram Diagonals Converse

• Parallelogram Opposite Sides Converse

• Parallelogram Opposite Angles Converse

• Opposite Sides Parallel and Congruent Theorem