## Properties of Parallelograms

This web page will help you discover some properties of parallelograms.

Before you begin, recall that a parallelogram is a quadrilateral whose opposite sides are parallel. Rhombuses, rectangles, and squares all fit this definition as well, so any properties you discover for parallelograms also apply to these shapes.

### Sketch

This sketch shows parallelogram LOVE and the measures of its angles. Drag vertices L, O, or V to change the parallelogram. If you drag a point off the screen, press Start Over to return it.

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Investigate

1. Change the shape of the parallelogram and watch the measures of the pairs of opposite angles. What do you notice about angles LOV and VEL? OVE and ELO?
2. Formulate the Parallelogram Opposite Angles Conjecture: The opposite angles of a parallelogram are _____.

Two angles that share a common side in a polygon are consecutive angles. For example, in parallelogram LOVE, angles LOV and OVE are a pair of consecutive angles.

3. Press Show Sums to see the sum of the measures of each pair of consecutive angles. What do you notice about the sum of consecutive angles?
4. Formulate the Parallelogram Consecutive Angles Conjecture: The consecutive angles of a parallelogram are _____.

5. Describe how to use the two conjectures you just made to find all the angles of a parallelogram with only one angle measure given.

### Sketch

This sketch shows parallelogram LOVE and the lengths of its sides. Drag vertices L, O, or V to change the parallelogram. If you drag a point off the screen, press Start Over to return it.

Sorry, this page requires a Java-compatible web browser. If you're using a recent version of your browser, be sure to check its Preferences or Options to make sure that Java content is enabled. Note: Java-compatible browsers are Internet Explorer and Opera.

Investigate

1. Change the shape of the parallelogram and watch the lengths of the opposite sides. What do you notice about sides LO and VE? OV and EL?
2. Formulate the Parallelogram Opposite Sides Conjecture: The opposite sides of a parallelogram are _____.

Press Show Diagonals to construct the diagonals LV and EO. The two diagonals intersect at point M.

3. Change the shape of the parallelogram and watch the lengths LM and VM. What do you notice about point M? Is this conclusion also true for diagonal EO?
4. Formulate the Parallelogram Diagonals Conjecture: The diagonals of a parallelogram _____.