# Worksheet: Diagonals of Parallelograms

Q1:

What can you say about the diagonals of a parallelogram?

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

Q2:

Is any quadrilateral whose diagonals bisect each other a parallelogram?

• Ayes
• Bno

Q3:

Are the two diagonals of a parallelogram perpendicular?

• Ano
• Byes

Q4:

Is the given quadrilateral a parallelogram?

• Ayes
• Bno

Q5:

Is the given quadrilateral a parallelogram?

• Ano
• Byes

Q6:

Given that , determine the length of .

Q7:

If is a parallelogram, find the value of .

Q8:

If is a parallelogram, find the value of .

Q9:

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
• Cyes, by
• Dyes, by
• Eyes, by

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 ,

Q10:

Find the value of in the following parallelogram.

Q11:

Find the value of in the following parallelogram.

Q12:

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

Q13:

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

Q14:

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

Q15:

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

Q16:

Given that and are two parallelograms, and the area of , find the area of .

Q17:

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 ,

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:

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

Q20:

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

Q21:

If is a quadrilateral, , , , and , find the midpoint of and , then determine what type of figure is.

• A , trapezoid
• B , parallelogram
• C , trapezoid
• D , parallelogram

Q22:

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