Definition: Congruent figures have exactly the same shape and size, so one can be moved onto the other by translations, reflections, and rotations.
What does congruent mean?
Two figures are congruent if all their matching sides and angles are equal. The symbol is a tilde over an equal sign.
How do you test it?
Check whether a sequence of rigid motions maps one figure exactly onto the other. For triangles, you can also compare side lengths: triangles with sides 5, 12, 13 and 13, 5, 12 are congruent.
How do you match the parts?
Corresponding parts line up. If triangle ABC is congruent to DEF, then AB = DE, BC = EF, CA = FD, and angle A = angle D.
What does an example show?
Triangle P is at (0, 0), (4, 0), (0, 3). Triangle Q is its reflection over the y-axis: (0, 0), (-4, 0), (0, 3). Q has the same side lengths 3, 4, 5, so they are congruent.
What does congruence not require?
The same position or orientation. A turned or flipped copy is still congruent.
What is a common mistake?
Confusing congruent with similar. Similar figures have the same shape but may differ in size. Equal angles alone do not make triangles congruent.