# Worksheet: Properties of Parallelograms

Q1:

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

• A
• B
• C
• D
• E

Q2:

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

• A
• B
• C
• D
• E

Q3:

In the parallelogram , , , and . Find the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

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

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

Q5:

How many altitudes are there in a parallelogram?

Q6:

In the figure shown, , , and . Determine and .

• A ,
• B ,
• C ,
• D ,

Q7:

Which of the following are a base and its corresponding altitude in the given parallelogram?

• A base: , altitude:
• B base: , altitude:
• C base: , altitude:
• D base: , altitude:

Q8:

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

• A
• B
• C
• D

Q9:

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

• A
• B
• C
• D
• E

Q10:

Find .

• A
• B
• C
• D

Q11:

Which of the following statements is not true?

• A Squares have four congruent angles and sides.
• B Opposite sides in a parallelogram are parallel.
• C Rhombuses have four congruent sides.
• D Parallelograms have exactly one pair of parallel sides.
• E Rectangles have four right angles.

Q12:

Find .

• A
• B
• C
• D

Q13:

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

• Afalse
• Btrue

Q14:

Find the lengths of and .

• A ,
• B ,
• C ,
• D ,

Q15:

In the figure, and are parallelograms. Find .

• A
• B
• C

Q16:

In parallelogram , suppose and . How are the lengths and related?

• A
• B
• C

Q17:

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

Q18:

In parallelogram , suppose . What is ?

Q19:

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

• Afalse
• Btrue

Q20:

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

Q21:

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

• Atrue
• Bfalse

Q22:

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

• A
• B
• C
• D

Q23:

Given that is a parallelogram, find .

Q24:

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 contains 2 pairs of parallel sides.
• EIt has 2 sets of perpendicular and parallel sides.

Q25:

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

• A
• B
• C
• D