Do you have trouble discerning all the different GEOMETRY figures in Fullerton?

From triangles to trapezoids, the seemingly limitless stream of shapes and subsequent formulas, postulates, and theorems can be overwhelming.

Let’s just focus on one of the more common yet confusing of GEOMETRY’s shapes: the quadrilateral.

GEOMETRY Shape Breakdowns

Many students confuse the meanings of quadrilateral and parallelogram. A quadrilateral at its basic definition is simply a shape with four sides. So in GEOMETRY, anything with four sides, four corners, and four angles is a quadrilateral.

Essentially, then, quadrilaterals are the most general of the four-shaped figures. All other four-sided shapes in GEOMETRY fit underneath the quadrilateral umbrella.

A parallelogram can be simple to discern because of its root word: parallel. Thus in GEOMETRY, a parallelogram is simply any four-sided shape with not one, but two pairs of parallel sides. It’s not enough for a four-sided figure to have only one pair of parallel sides; trapezoids, for example, fail this parallelogram test.

Some common parallelograms include several famous figures – namely, the square, rectangle, and rhombus. Every shape with four sides, four corners, and four angles starts with the quadrilateral, and then gets gradually more specific.

So if we’re keeping track of what “fits” inside of what, here’s a helpful line to remember:

QUADRILATERALS -> PARALLELOGRAMS -> SQUARES/RECTANGLES/RHOMBUSES

Trapezoids, kites, and other quadrilaterals do not pass the parallelogram test because they do not have two pairs of parallel sides. In the case of a kite, this quadrilateral actually contains zero pairs of parallel sides. So, the kite is a quadrilateral and a quadrilateral alone.

GEOMETRY Shape Suggestions

If you ever get confused about the differences among quadrilaterals, always go back to the basic question: does the shape have four sides? If yes, you have a quadrilateral.

Next, ask: how many pairs of parallel sides does the four-sided shape have? If the answer is zero, then you merely have a quadrilateral. If you have exactly one pair of parallel sides, then you have a trapezoid, which is not a parallelogram. If you have two, congratulations! You have a parallelogram.

Finally, if you do indeed have two pairs of parallel sides, ask yourself: are all the side lengths and angle measures equal? Here’s how squares, rectangles, and rhombuses compare:

Square: equal side lengths and equal angle measures (each totaling 90 degrees)

Rectangle: equal angle measures (each totaling 90 degrees) and two pairs of equal length sides

Rhombus: equal side lengths and two pairs of equal angle measures

If quadrilaterals still confuse you, as a GEOMETRY tutor I highly encourage flash cards!

As with any concept in GEOMETRY or other math courses, practice makes perfect.

Take it one shape at a time, and gradually learn them all.

Looking for a GEOMETRY tutor in Fullerton or other surrounding locations? Check out www.APlusInHomeTutors.com to find a great tutor today!