# 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.

**Q5: **

Given that is a parallelogram and , find .

**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.

**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