# Worksheet: Diagonals of Parallelograms

In this worksheet, we will practice correlating between the diagonals of parallelograms and using these properties to find unknown measures.

**Q1: **

Given that , determine the length of .

**Q3: **

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

**Q4: **

What can you say about the diagonals of a parallelogram?

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

**Q5: **

Is any quadrilateral whose diagonals bisect each other a parallelogram?

- Ano
- Byes

**Q6: **

Are the two diagonals of a parallelogram perpendicular?

- Ayes
- Bno

**Q7: **

If is a parallelogram, find the value 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 both triangles. Using the information from the earlier parts of the question, can we prove that triangles and are congruent? If yes, by which congruence criteria?

- ANo
- BYes, by SAS
- CYes, by ASA
- DYes, by HL
- EYes, by SSS

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: **

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

**Q10: **

In a parallelogram , the coordinates of , , and are , , and , respectively. Find the coordinates of the point at which the two diagonals intersect, and then determine the coordinates of point .

- A ,
- B ,
- C ,
- D ,

**Q11: **

is a parallelogram where the coordinates of are and the coordinates of are . Find the coordinates of the point of intersection of the two diagonals of .

- A
- B
- C
- D

**Q12: **

In parallelogram , the coordinates of are and those of the intersection of the diagonals are . What are the coordinates of point ?

- A
- B
- C
- D
- E

**Q14: **

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

**Q15: **

If is a parallelogram, find the value of .

**Q16: **

is a parallelogram where the coordinates of are and the coordinates of are . Find the coordinates of the point of intersection of the two diagonals of .

- A
- B
- C
- D

**Q17: **

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

**Q18: **

In a parallelogram , the coordinates of , , and are , , and , respectively. Find the coordinates of the point at which the two diagonals intersect, and then determine the coordinates of point .

- A ,
- B ,
- C ,
- D ,

**Q19: **

The perimeter of the rectangle is the same as the perimeter of the square.

What is the area of the square?

**Q20: **

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

**Q22: **

Given that is a rectangle, where and , find .

**Q23: **

In this rectangle, , , and . Find the value of .

**Q24: **

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