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.
- BWe cannot decide without more information.
- CIt is a rectangle.

**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