How do the properties of transformations assist in solving geometric problems?

The selected answer highlights the important role of transformations in deriving properties of geometric figures from known shapes. By applying transformations such as translations, rotations, reflections, and dilations, one can explore how certain properties remain invariant or change, thus deepening understanding of geometric relationships. For instance, when a triangle is rotated or reflected, the fundamental properties such as angles and side lengths remain unchanged, allowing for conclusions to be drawn about similar figures or congruence.

Using known shapes as a basis can also simplify problem-solving; for example, if a student knows how to calculate the area of a rectangle, understanding that a parallelogram can be transformed into a rectangle can lead them to derive the area of the parallelogram through established formulas. Overall, transformations serve as a powerful tool for analyzing and understanding geometric structures, articulating relationships, and providing a solid foundation for further explorations in geometry.