What Does "Congruent" Mean in Math?
In mathematics, congruent means that two figures or objects have the same shape and size. They can be exactly matched by moving, rotating, or flipping one figure without changing its size or shape.
Key Points:
- Congruent shapes have equal corresponding sides and equal corresponding angles.
- Congruence is often denoted by the symbol ≅. For example, if triangle ABC is congruent to triangle DEF, we write:
△ABC≅△DEF\triangle ABC\cong \triangle DEF△ABC≅△DEF
- Congruence applies to various geometric figures such as triangles, polygons, and segments.
Examples:
- Two line segments are congruent if they have the same length.
- Two triangles are congruent if all their corresponding sides and angles are equal.
Summary:
Congruent = Same shape + Same size If you imagine cutting out a shape from paper, you can place it exactly over another congruent shape without any gaps or overlaps. If you'd like, I can explain how to prove congruence between triangles or other shapes!
