"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.



Proof:

  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.

Extension:

  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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