What you’ll learn
Prove rectangle properties.
Key idea
Then verify adjacent sides perpendicular using finite slope product negative one or a zero dot product.
Parallelogram alone is insufficient; add the right-angle condition.
Worked example
Complete missing statements or reasons in a proof for 'Prove rectangle properties'.
Consecutive coordinate vertices are A=(-2, 1), B=(0, 4), C=(-6, 8), D=(-8, 5). Complete a rectangle proof with both the parallelogram and right-angle conditions.
- AB/CD slope 3/2, BC/AD slope -2/3, and 3/2*-2/3=-1.
- Both opposite pairs are parallel and adjacent directions are perpendicular, hence rectangle.
Answer: Opposite pairs parallel and adjacent sides perpendicular — AB/CD slope 3/2, BC/AD slope -2/3, and 3/2*-2/3=-1.
Quick Check
Complete missing statements or reasons in a proof for 'Prove rectangle properties'.
Consecutive coordinate vertices are A=(0, 0), B=(2, 2), C=(-4, 8), D=(-6, 6). Complete a rectangle proof with both the parallelogram and right-angle conditions.