Congruent Polygons: Definition & Examples

Instructor: Joseph Vigil
In this lesson, you'll review what polygons are, and you'll discover the conditions that polygons must meet in order to be congruent. Then, you can test your knowledge with a brief quiz.

Anna and Alicia

Anna and Alicia are twin sisters. Everything one gets, the other has to get. At the store, when their parents buys candy for one, they have to buy candy for the other. So if Anna gets a candy bar…

If Anna gets this candy bar...
rectangular candy bar

Then Alicia asks for the same candy bar

...then Alicia gets the same candy bar.
rectangular candy bar

These bars are rectangular in shape:

the rectangular exterior of the candy bar
rectangular exterior of the candy bar

When we put the two rectangular bars side by side, we can see that they're congruent, or equal in size and shape.

The candy bars--or rectangles--are congruent!
candy bars side by side

In order for two shapes to be congruent, they must meet a couple of conditions:

  1. The sides in one shape must be equal to the sides in the second shape.
  2. The angles in one shape must be equal to the angles in the second shape.

As we can see above, the sides of the second bar are all the same length as the sides of the first bar, and the angles in the second bar are all the same as the angles in the first bar.

So every time Anna gets something, Alicia has to get an object that is congruent to what Anna gets, and vice versa.

Polygon Break

Before we continue with Anna and Alicia's story, let's take a break to define what a polygon is.

A polygon is a closed shape with straight sides. So, many familiar shapes such as triangles, squares, and rectangles are polygons because they're closed shapes, and all their sides are straight.

Circles and ovals, though, are left out because their exterior is one large arc. Although they're closed shapes, they don't have any straight sides, so they're not polygons.

The Fancy Mirror

The twins' parents bought them each a fancy framed mirror to hang in their bedrooms.

a rectangular framed mirror for Anna
framed mirror

Anna wants to hang hers vertically, just the way it looks above.

But Alicia wants to be different and hang hers horizontally:

same mirror arranged horizontally
same mirror arranged horizontally

Up till now, everything the girls had was congruent. But now, their rectangular mirrors are hanging in different directions:

One hangs vertically, and the other hangs horizontally. Congruent?
mirrors side by side

But wait! Remember our two conditions for congruency:

  1. The sides in one shape must be equal to the sides in the second shape.
  2. The angles in one shape must be equal to the angles in the second shape.

The sides of one mirror are the same length as the sides in the other mirror, and both mirrors contain four right angles. Although one lies horizontally in comparison to the other, they still meet the two conditions for congruency, so they're still congruent.

Orientation, or the direction a polygon faces, does not affect congruency.

This rule is true of any polygon. Let's look at these arrows:

These arrows face opposite directions.
arrows facing opposite directions

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