Definition:
Polygons
are congruent when they have the same number of sides, and all corresponding sides and
interior angles
are congruent.
The polygons will have the same shape and size, but one may be a rotated, or be the mirror image of the other.

**Note:** This entry deals with the congruence of polygons in general. Congruent triangles are discussed in more depth in
Congruent Triangles.

Polygons are congruent if they are equal in all respects:

- Same number of sides
- All corresponding sides are the same length,
- All corresponding interior angles are the same measure.

One way to think about this is to imagine the polygons are made of cardboard. If you can move them, turn them over and stack them exactly on top of each other, then they are congruent. To see this, click on any polygon below. It will be flipped over, rotated and stacked on another as needed to demonstrate that they are congruent.

Try this
Click on 'Next' or 'Run'. Each polygon in turn will be flipped over, rotated and stacked on another as needed to show that it is congruent to it.

Mathematically speaking, each operation being done on the polygons is one of three types:

### Rotation

This is where the polygon is rotated about a given point by a certain amount. In the applet above, the rotations are around a point inside the polygon, but any point can be chosen. While rotations are being done, this point is shown. See Rotation.### Reflection

When the polygon is 'flipped over' above, this operation is called reflection. In essence the polygon is 'reflected' over a given line. It's as if the points on each side of the line are mirror imaged, thinking of the line as the mirror. In the above applet, the line of reflection is shown while the operation is going on. Reflection.### Translation

When the polygon is moved from one point to another, this is called 'translation'. When the polygon is translated, it is moved, but without any rotation. Translate.

The three types of operation above are called 'transforms'. In effect, they transform a shape to another by changing it in some way - rotation, reflection and translation.

- Congruent triangles
- Tests for congruence
- Why AAA (angle-angle-angle) doesn't work
- Why SSA (side-side-angle) doesn't work

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