"The measure of each angle of a rectangle is 90."

A Proof Outline
by David Wise

Note: I recommend that this page be printed out, so that the instructions are easier to follow.

In order to successfully complete a proof, it is important to think of the definition and the construction of a rectangle.
In the following outline, I will provide the statements, you provide the reasons.

Prove: If a quadrilateral is a rectangle, then the measure of each angle of the rectangle is 90.

Given: Rectangle ABCD. Prove: Angles BAD = 90, CBA = 90, DCB = 90, and ADC = 90.

• A rectangle is a parallelogram, so the definition and properties of a parallelogram apply to a rectangle.
• Consider how a rectangle is constructed------parallel lines.
• Consider properties of parallel lines.
• Click here to investigate this sketch to help with the steps of the proof.

Proof:

1. Angles BAD, CBA, DCB, and ADC are all congruent to each other.
2. Angle BAD + angle CBA + angle DCB + angle ADC = 360.
3. Angles BAD = 90, CBA = 90, DCB = 90, and ADC = 90.

Extension:

1. Transform the two-column proof into a paragraph proof.
2. Find an alternative way to prove that the measure of each angle of a rectangle is 90.

If you have any questions while trying to complete this investigation, or suggestions that would be useful, especially for use at the high school level, please send e-mail to esiwdivad@yahoo.com.