What Does Congruent Mean?

In math, especially geometry, congruent means having exactly the same shape and size. Two figures are congruent if you could slide, rotate, or flip one so it lands perfectly on top of the other, matching completely.

Key points:

• The symbol for congruent is ≅ (an equals sign with a tilde on top). For example, △ABC ≅ △DEF means triangle ABC is congruent to triangle DEF.
• Same size AND shape. All corresponding sides are equal in length and all corresponding angles are equal.
• Position/orientation doesn't matter. A shape can be rotated or mirrored and still be congruent to the original.

Congruent vs. similar:

• Congruent = same shape and same size (identical copies).
• Similar = same shape but different size (one is a scaled version of the other), using the symbol ~.

Congruent vs. equal: "Equal" (=) is usually used for numbers and measurements (like side lengths or angle degrees), while "congruent" (≅) is used for the figures themselves. So we'd say two segments are congruent, but their lengths are equal.

Everyday meaning: Outside of math, "congruent" is also used more loosely to mean "in agreement" or "consistent" — for example, "her actions were congruent with her values."