# Worksheet: Properties of Parallelograms

In this worksheet, we will practice determining whether a quadrilateral is a parallelogram or not and using the properties of parallelograms to find unknown angles or lengths.

Q1:

Is the following statement true or false? In a parallelogram, opposite sides are parallel and equal in length.

• Atrue
• Bfalse

Q2:

Determine whether this statement is true or false: All parallelograms are regular polygons.

• Atrue
• Bfalse

Q3:

Which of the following statements correctly describes a property of the given shape? • AIt is equilateral.
• BIt contains 2 pairs of perpendicular sides.
• CIt has 4 angles equal in measure.
• DIt has 2 sets of perpendicular and parallel sides.
• EIt contains 2 pairs of parallel sides.

Q4:

Find the lengths of and . • A,
• B,
• C,
• D,

Q5:

Given that is a parallelogram and , find . Q6:

In the figure below, given that is a parallelogram, determine . Q7:

In the figure below, given that is a parallelogram, find . Q8:

is a parallelogram such that , , and . Determine the coordinates of vertex .

• A
• B
• C
• D
• E

Q9:

Which of the following statements must be true about a parallelogram?

• AIt has one pair of parallel sides.
• BIt has four congruent sides.
• CIt has four sides of equal length.
• DIt has four right angles.
• EIt has two pairs of parallel opposite sides.

Q10:

In the parallelogram , , , and . Find the values of and . • A,
• B,
• C,
• D,
• E,

Q11:

What is the sum of the measures of any two consecutive angles in a parallelogram?

Q12:

In the following figure is a parallelogram. What is the measure of ? Q13:

Find . Q14:

In the figure, and are parallelograms. Find . Q15:

Given that is a parallelogram, find the area of triangle . Q16:

is a parallelogram, where the coordinates of the points , , and are , , and , respectively. Find the coordinates of the vertex .

• A
• B
• C
• D

Q17:

In the figure shown, , , and . Determine and . • A,
• B,
• C,
• D,

Q18:

Find . Q19:

In parallelogram , suppose . What is ?

Q20:

Given that is a parallelogram, find . Q21:

In parallelogram , suppose and . How are the lengths and related? • A
• B
• C

Q22:

How many altitudes are there in a parallelogram?

Q23:

Which of the following are a base and its corresponding altitude in the given parallelogram? • Abase: , altitude:
• Bbase: , altitude:
• Cbase: , altitude:
• Dbase: , altitude:

Q24:

Which of the following statements is not true?

• AOpposite sides in a parallelogram are parallel.
• BRhombuses have four congruent sides.
• CParallelograms have exactly one pair of parallel sides.
• DSquares have four congruent angles and sides.
• ERectangles have four right angles.

Q25:

Is the following statement true or false? In a parallelogram, there is a pair of opposite sides that do not have to be parallel.

• Atrue
• Bfalse