# Lesson Worksheet: Properties of Parallelograms Mathematics

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:

In parallelogram , , , and . What is the perimeter of ? Q2:

If is a parallelogram, find the value of . Q3:

Find the value of in the following parallelogram. Q4:

In the figure below, given that is a rectangle, is a parallelogram, and , find the length of . Q5:

What can you say about the diagonals of a parallelogram?

• AThey are equal in length.
• BThey bisect each other.
• CThey are perpendicular.

Q6:

Given that is a parallelogram and , find the perimeter of . Q7:

Given that , determine the length of . Q8:

The given figure shows a parallelogram . Using what you know about alternate angles, determine which angle will have the same measure as .

• A
• B
• C
• D
• E

Which angle will be equal in measure to ?

• A
• B
• C
• D
• E

is a common side to triangle and triangle . Using the information from the earlier parts of the question, can we prove that triangles and are congruent? If yes, by which congruence criteria?

• AYes, by ASA
• BNo
• CYes, by SAS
• DYes, by SSS
• EYes, by HL

What will be true of and and of and ?

• A,
• B,
• C,
• D,

What will be true of angles and and of angles and ?

• A,
• B,
• C,
• D,

Q9:

The lengths of two adjacent sides of a parallelogram are units and units. Write an expression for its perimeter.

• A units
• B units
• C units
• D units
• E units

Q10:

Is any quadrilateral whose diagonals bisect each other a parallelogram?

• AYes
• BNo