# 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