Circles Part 1: Similarity Intuition #JulyChallenge2014 5/31
All circles are similar, right?
Okay, maybe it’s not given. In fact, it needs to be proven. This proof is yet another that is so easily demonstrated with dynamic math tools (like desmos and geogebra
So long as you can move one center onto the other (translate) and dilate one radius to equal the other, similarity is achieved. This works for every circle. The perfect proportional balance achieved with circles lays the foundation for most of not all relationships found in them.
Similarity gives us a simple system for comparing measures in multiple figures.
You can even explore this with repetition of congruent triangles:
Below are a couple of applications that push further with exploring the measures of circles, proportionality, and relationships in the measures.
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