Explore the principles and applications of geometry, including shapes, theorems, and real-world problem-solving.
Shapes can be congruent (exactly the same size and shape) or similar (same shape but different sizes).
Two shapes are congruent if they can be matched exactly using rotations, reflections, or translations. Their corresponding sides and angles are identical.
Shapes are similar if their angles are equal and their sides are proportional. This concept helps us create scale models and maps.
We use criteria like SSS (Side-Side-Side), SAS (Side-Angle-Side), and AA (Angle-Angle) to prove if triangles are congruent or similar.
Engineers use these concepts to create models and blueprints, ensuring everything fits together perfectly!
\[\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\]
Designing a scaled-down model of a building.
Ensuring puzzle pieces fit together perfectly.
Congruence means exact match; similarity means same shape, different size.