Congruent is a new term for an idea we have already been using. We say that two figures are congruent if one can be lined up exactly with the other by a rigid transformation.

For example, triangle is congruent to triangle because they can be matched up by reflecting triangle across followed by the translation shown by the arrow. Notice that all corresponding angles and side lengths are equal.

Triangle A B C, triangle A B prime C, dashed arrow from B prime to point F and triangle E F D. Triangle A B prime C is the image of triangle A B C after reflection over A C. Angle A is 63 point 4 degrees, angle B is 71 point 6 degrees and angle C is 45 degrees. Side A B is 2 point 2 4, side B C is 2 point 8 3 and side A C is 3 point 0 0. Angle E is 63 point 4 degrees, angle F is 71 point 6 degrees and angle D is 45 degrees. Side E F is 2 point 2 4, side F D  is 2 point 8 3 and side D E is 3 point 0 0.

Here are some other facts about congruent figures:

• We don’t need to check all the measurements to prove two figures are congruent. We just have to find a rigid transformation that matches up the figures.
• A figure that looks like a mirror image of another figure can be congruent to it. This means there must be a reflection in the sequence of transformations that matches up the figures.
• Since two congruent polygons have the same area and the same perimeter, one way to show that two polygons are not congruent is to show that they have a different area or perimeter.