Congruence in Geometry

Congruence means two shapes are exactly the same in size and shape, even if they are flipped, rotated, or moved. Think of two puzzle pieces that fit perfectly together—if you can place one over the other and they match up exactly, they are congruent.

To prove congruence between triangles, we often use shortcuts like SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle). If all corresponding sides and angles are equal, the shapes are congruent.

Similarity in Geometry

Similarity means two shapes have the same shape, but not necessarily the same size. Their angles are equal, and their sides are proportional. Imagine shrinking or enlarging a photo—everything looks the same, just bigger or smaller.

Key Differences

• Congruence: Same size and shape.
• Similarity: Same shape, different size.

Real-World Uses

• Architects use congruence to ensure parts fit exactly.
• Engineers use similarity to scale models of bridges or buildings.