Parallelograms, and Rectangles: Finding Segments, and Angles.

How often when solving a problem that involves the properties of a parallelogram, have you felt lost?...How is this? Should I state that the angles are congruent, or that they are supplementary? Are the diagonals bisecting each other? How are the two consecutive angles?

In the development of this lesson, you will be given many visual clues, and hints that will enable you to solve any problem that involves the properties of a parallelogram. Several of the explained examples take a great deal of an effort to show you the algebra that is involved, so that you don't get lost. This lesson is really on your side!

Lesson's Content

Lesson's Glossary

Angle
Geometric shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

Parallelogram
Any quadrilateral with two pairs of opposite sides parallel.

Polygon
It is a closed plane figure with a least three straight segments as sides.

Quadrilateral
A four-sided polygon.

Rectangle
A quadrilateral whose angles are all right angles.

Segment
Line segment; A section of a line, defined by two end points and all the points between them.

Interactive Geometric Applets: Relevant Theorems.

In a parallelogram you have properties that allow you to solve for angles, and sides

in the parallelogram. Some of these are opposite sides parallel and congruent, opposite

angles congruent, consecutive angles supplementary, and diagonals bisect each other.

Follow the directions in this interactive geometric applet to check all of them.

A rectangle is a special parallelogram that has all angles right and congruent. It has

congruent diagonals, that bisect forming four congruent segments. Opposite sides

are parallel and congruent. Interact with this great geometric applet to generate

multiple instances of rectangles and appreciate how it complies with all these properties.

Vocabulary Puzzle Interactive

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