"The consecutive angles of a parallelogram are supplementary."

A Proof Outline
Using Geometer's Sketchpad
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 parallelogram.
In the following outline, I will provide the statements, you provide the reasons.

Prove: *If a quadrilateral is a parallelogram, then the consecutive angles are supplementary.

Given: Parallelogram ABCD

Prove: Angle BAD and angle CBA are supplementary. *This is a proof for a single pair of consecutive angles. To fully prove the statement above, the 3 other pairs of consecutive angles must also be proved to be supplementary.


  1. Angle BAD is congruent to angle GCB.
  2. Angle GBC and angle CBA are supplementary.
  3. Angle GBC + angle CBA = 180
  4. Angle BAD + angle CBA = 180
  5. Angle BAD and angle CBA are supplementary.


  1. Use the previous proof as an example to prove that the remaining three pairs of consecutive angles of a parallelogram are supplementary.
  2. Transform the two-column proof above and in extension 1. into a paragraph proof.

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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