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 Math formula about the Math formula -axis.

Math diagram

The polygons Math formula and Math formula are congruent figures. That is, Math formula .

Now, rotate the polygon Math formula by Math formula about the origin.

Math diagram

Again, Math formula .

By the transitive property of congruence, Math formula .

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

Here, the hexagon Math formula is congruent to hexagon Math formula .

Math diagram

Note that the order in which you write the vertices matters; for instance, hexagon Math formula is not congruent to hexagon Math formula .

Also see congruent triangles .


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