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.

- Consider how a parallelogram is constructed------parallel lines.

- Consider properties of parallel lines, linear pairs, and vertical angles.
**Click here**to investigate this sketch to help with the steps of the proof.

**Proof****:**

- Angle BAD is congruent to angle GCB.
- Angle GBC and angle CBA are supplementary.
- Angle GBC + angle CBA = 180
- Angle BAD + angle CBA = 180
.**Angle BAD and angle CBA are supplementary**

**Extension****:**

- Use the previous proof as an example to prove that the remaining three pairs of consecutive angles of a parallelogram are supplementary.
- 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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