Worksheet: Proving That Parallelograms Are Rectangles

In this worksheet, we will practice determining if a parallelogram is a rectangle in terms of its sides, angles, and/or diagonals.

Q1:

A quadrilateral has vertices at , , , and .

Decide if the quadrilateral is a parallelogram by calculating the length of each side.

• AIt is a parallelogram.
• BIt is not a parallelogram.

Decide if the quadrilateral is a rectangle by calculating the length of its diagonals.

• AIt is a rectangle.
• BIt is not a rectangle.

Q2:

A parallelogram has vertices , , , and .

Calculate the length of . Give an exact answer.

• A13
• B
• C7
• D

Calculate the length of . Give an exact answer.

• A7
• B13
• C
• D

Hence, state whether or not the parallelogram is a rectangle.

• AIt is not a rectangle.
• CIt is a rectangle.

Q3:

A parallelogram has vertices at the coordinates and .

Work out the length of the diagonal .

Work out the length of the diagonal .

Using these lengths, is the parallelogram a rectangle?

• Ano
• Byes

Q4:

A parallelogram has vertices at the coordinates and .

Work out the slope of .

Work out the slope of .

Work out the product of the slopes from parts (a) and (b).

Is a rectangle?

• Ayes
• Bno