Properties of a Parallelogram

Definition: A parallelogram is a quadrilateral with parallel opposite sides. Rectangles, rhombi and squares are all parallelograms.

A parallelogram has the following properties:
– Opposite sides are congruent and parallel
– Opposite angles are congruent
– Diagonals bisect each other
– Consecutive angles are supplementary

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Example: Find the lengths of side BC and side DC
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Solution:

Use the given information to determine the side lengths of sides BA and AD.

Step 1: The figure indicates that this quadrilateral has two pairs of parallel lines, so we can conclude that it is a parallelogram

Step 2: Since parallelograms have two pairs of congruent sides, we know side BA is congruent to side CD,
and side BC is congruent to side AD.

Step 3: Since side AB = 5 mm, then CD must also have a length of 5 mm
Since side AD = 3 + 4 = 7 mm, then side BC must also equal 7mm.

Based on the properties of a parallelogram, we can conclude that side BC = 7mm, side DC = 5mm.

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