Similar Triangles:
Similar triangles are two triangles that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion. In other words, the ratio of the lengths of corresponding sides in similar triangles remains the same.

Congruent Triangles:
Congruent triangles are two triangles that are identical in shape and size. They have the same angles and the same side lengths. If two triangles are congruent, it means that all corresponding angles and sides of both triangles are equal.

Differences between Similar Triangles and Congruent Triangles:

1. Size: The primary difference between similar and congruent triangles lies in their size. Similar triangles have proportional side lengths, while congruent triangles have exactly the same side lengths.

2. Corresponding Angles: In similar triangles, corresponding angles are equal, but they may differ in size. In congruent triangles, corresponding angles are not only equal but also have the same size.

3. Corresponding Sides: Similar triangles have corresponding sides that are in proportion. Congruent triangles have corresponding sides that are exactly equal in length.

4. Shape: Similar triangles have the same shape but may differ in size. Congruent triangles have the same shape and size, making them identical.

5. Notation: When representing similar triangles, a symbol (~) is used between their names. For example, if triangle ABC is similar to triangle DEF, it can be written as ΔABC ~ ΔDEF. Congruent triangles are represented using an equals sign (=). For example, if triangle XYZ is congruent to triangle PQR, it can be written as ΔXYZ = ΔPQR.

6. Transformations: Similar triangles can be obtained through transformations such as dilation or stretching. Congruent triangles can be obtained through rigid transformations, including translation, rotation, and reflection.

7. Proportional Sides: In similar triangles, the ratios of corresponding sides are equal. This property is not applicable to congruent triangles, as their corresponding sides are exactly equal.

In conclusion, similar triangles have the same shape but may differ in size, while congruent triangles are identical in both shape and size. Similar triangles have proportional corresponding sides and equal corresponding angles, whereas congruent triangles have corresponding sides and angles that are exactly equal.

Similar figures and congruent figures both have the same shape. The difference between similar figures and congruent figures is that congruent figures also have the same size. So, corresponding sides and corresponding angles of congruent figures have the same measures.