# Lesson Worksheet: Special Quadrilaterals Mathematics

In this worksheet, we will practice using the properties of special quadrilaterals to solve problems involving algebraic expressions, equations, and coordinates.

Q1:

Given that , determine the length of . Q2:

Find the value of in the following parallelogram. 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 bisect each other.
• CThey are perpendicular.

Q5:

Is any quadrilateral whose diagonals bisect each other a parallelogram?

• AYes
• BNo

Q6:

Are the two diagonals of a parallelogram perpendicular?

• ANo
• BYes

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 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:

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

Q13:

Find the value of in the following parallelogram. 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 . Q21:

If , , , and , what values of and make parellelogram a rectangle? • A,
• B,
• C,
• D,
• E,

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

Q25:

is a parallelogram. Given that the perimeter of is 54, find the length of . 