Reasoning and Proof through Similarity

Have you ever zoomed in on a photo and noticed how the shapes stay the same, just bigger? Or watched a character move across a screen in an animated movie? That’s similarity in action: when shapes grow or shrink but keep the same angles and proportions. Architects use it to design buildings. Animators use it to make movement look real. Scientists use it to study things like shadows and reflections. In this badge, you’ll explore how shapes are connected and how we can prove that two shapes are similar. In M153 Geometry: Reasoning and Proof through Similarity, you will construct and critique logical arguments as you explore relationships between geometric figures. You will perform geometric constructions and describe a sequence of transformations to prove that one figure is similar to another, using technology to aid in performing transformations. You will also test and apply theorems to reason about relationships between figures to prove similarity, as well as to construct visual representations of images your mind creates using segments, angles, triangles, or quadrilaterals. Acquiring the skills of geometric reasoning in these areas leads to the understanding of analytical approaches to geometry and opportunities for applying logical reasoning in fields beyond mathematics. Similarity is useful for careers in a variety of fields, like mathematics, graphic design, animation, art, and physics.

Suggested prerequisites for this badge: basic understanding of angles, triangles, and quadrilaterals.