Proving Quadrilaterals Are Parallelograms

If you can prove that one pair of opposite sides of a parallelogram are the same length and have the same slope, you can prove that it is a parallelogram.

• Always

• Sometimes

• Never

How can you prove two diagonals bisect each other?

• Use distance formula and prove they have the same length

• Use midpoint formula and prove they have the same midpoint

• Use the slope formula and prove they have the same slope

• Use the slope formula and prove the slopes are perpendicular

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

• 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. 

Is the quadrilateral a parallelogram?

• Yes

• No

• Not enough information.

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

• x = 8

• x = 26

• x = 28

• x = 38

Determine the value of x that would classify this quadrilateral as a parallelogram.

• x = 50

• x = 45

• x = 30

• x = 25

In order for ABCD to be a parallelogram, what must the value of x be?

• 132

• 66

• 114

• 48

Determine the value of x and y that would classify this quadrilateral as a parallelogram. 

• x = 9 ; y = 16

• x = 16; y = 9

How long is the side CD?

• 7

• 3

• 35

• 27

Which of the following cannot be used to prove a shape is a parallelogram?

• Both pairs of opposite sides parallel

• Both pairs of opposite sides congruent

• One pair of opposite sides congruent

• Both pairs of opposite angles congruent