What are Differences between Similar triangles and Congruent Triangles?

Similar triangles and Congruent triangles are both concepts in geometry, but they have distinct differences:

1. Definition: Similar triangles have the same shape but may differ in size. Congruent triangles, on the other hand, are identical in both shape and size.
2. Size: In similar triangles, corresponding angles are equal, and corresponding sides are proportional, meaning their lengths have the same ratio. In incongruent triangles, all corresponding angles and sides are equal in length.
3. Notation: Similar triangles are denoted using the symbol “~” (tilde), while congruent triangles use the symbol “≅” (congruent).
4. Number of Solutions: Similar triangles can have an infinite number of solutions as long as their angles remain the same, and their sides maintain a consistent ratio. Congruent triangles have only one solution because all corresponding parts are exactly equal.
5. Applications: Similar triangles are often used in applications like scale models, mapmaking, and trigonometry to solve problems involving proportions. Congruent triangles are used to prove geometric properties and are foundational in geometric proofs.

In summary, the key difference is that similar triangles have proportional sides and equal angles, whereas congruent triangles have the same shape and size with equal sides and angles