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 opposite sides are congruent.

Given: Parallelogram ABCD

**Prove: Segment AD is congruent
to segment BC and segment AB is congruent to segment DC.**

- Consider how a parallelogram is constructed------parallel lines.
- Consider properties of parallel lines.
- Construct a diagonal of the parallelogram to create 2 triangles.
- Consider triangle congruency properties.

**Click here**to investigate this sketch to help with the steps of the proof.

**Proof****:**

- Angle DBA is congruent to angle BDC.

- Angle ADB is congruent to angle CBD.

- Triangle ABD is congruent to triangle CDB.
**Segment AD is congruent to segment BC and segment AB is congruent to segment DC.**

**Extension****:**

- Transform the two-column proof into a paragraph proof.
- Find an alternative way to prove that the opposite side of a parallelogram are congruent.

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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