Reasoning and Proof through Congruence

If two images look the same to the human eye, does that make them identical? In this badge, you’ll explore how shapes, especially triangles, can be exactly the same in size and shape (that’s called congruent), even when they’ve been flipped, rotated, or slid around. You’ll learn how to prove when triangles are congruent using powerful shortcuts, and then use those proofs to crack the code on unknown angles and side lengths. Learning how to confidently argue why two shapes match up perfectly is a useful skill for real world geometry. In M152 Geometry: Reasoning and Proof through Congruence, you will construct and critique logical arguments as you explore relationships between geometric figures. You will perform geometric constructions and describe a sequence of rigid motions to prove that one figure is congruent with another, using technology to aid in performing constructions and transformations. Acquiring the skills of geometric reasoning in these areas leads to the understanding of analytical approaches to geometry and opportunities to apply logical reasoning in fields beyond mathematics. Congruence 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.