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.
- Consider properties of quadrilaterals.
**Click here**to investigate this sketch to help with the steps of the proof.

**Proof****:**

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

**Extension****:**

- Transform the two-column proof into a paragraph proof.
- 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**.

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