Parallelograms

In parallelogram ABCD, AB is parallel to_______.

• ED

• DC

• BC

• AD

Answer explanation

In parallelograms, opposite sides are parallel

• GI
  

• FG

• IJ

• GH

Answer explanation

In parallelograms, the diagonals bisect one another.

What are the coordinates of the intersection of the diagonals of parallelogram WXYZ with vertices W(−1, 2), X(3, 2), Y(5, −1), and Z(1, −1)? (HINT: find the midpoint of a diagonal).

• (-1, 2)

• (-3, 1.5)

• (2, 0.5)

• (1, 1.5)

Answer explanation

Use the midpoint formula

$\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)$

In parallelogram ABCD, which pair of angles are not supplementary?

• B, C

• D, B

• D, C

• A, D

Answer explanation

In parallelograms, opposite angles are congruent, consecutive angles are supplementary.

• 127

• 123

• 110

• 120

Answer explanation

Opposite angles are congruent

The coordinates of the vertices of WXYZ are W(-3, 3), X(6, 6), Y(1, 0), and Z(-5, -2).Determine if WXYZ is a parallelogram. Explain. (HINT: use slope)

• No. WZ is not parallel to XY.

• Yes. The two diagonals bisect each other.

• Yes. The two sets of opposite sides are parallel.

• No. WX is not parallel to ZY.

Answer explanation

In parallelograms, both sets of opposite sides have to have the same slope (aka they are parallel)

The quadrilateral below is a parallelogram because_______.

• both pairs of opposite sides are congruent

• both pairs of opposite angles are congruent

• it has four sides

• it was feeling extra parallelogrammy today

Answer explanation

In parallelograms, opposite angles are congruent.

The quadrilateral below is a parallelogram because_______.

• it is a square

• the diagonals are perpendicular

• the diagonals are not congruent

• the diagonals bisect each other

Answer explanation

If the diagonals bisect one another, the quadrilateral is a parallelogram.

Which of the following does not guarantee that a quadrilateral is a parallelogram?

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• A pair of consecutive sides are congruent.

• Both pairs of opposite sides are parallel.

Find the values of x and y that ensure that the quadrilateral is a parallelogram.

• x = 12, y = 13

• x = 16, y = 26

• x = 13, y = 12

• x = 16, y = 12