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Congruent Figures

Congruent figures are geometric figures that have the same shape and size. That is, if you can transform one figure into another figure by a sequence of translations , rotations , and/or reflections , then the two figures are congruent.

If the figures are polygons, then they are congruent if all the corresponding sides and corresponding angles are congruent.

Math diagram

Consider the polygon shown.

Math diagram

Reflect the polygon P 1 about the y -axis.

Math diagram

The polygons P 1 and P 2 are congruent figures. That is, P 1 P 2 .

Now, rotate the polygon P 2 by 270 ° about the origin.

Math diagram

Again, P 2 P 3 .

By the transitive property of congruence, P 1 P 3 .

Therefore, the polygon obtained by the transformations is congruent to the initial polygon.

Here, the hexagon A B C D E F is congruent to hexagon J K L M N O .

Math diagram

Note that the order in which you write the vertices matters; for instance, hexagon A B C D E F is not congruent to hexagon O J K L M N .

Also see congruent triangles .


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