Unit two is about proving the congruence of angles, sides, and triangles and using these congruent relationships to prove properties of parallel lines, triangles, and other polygons. Throughout the unit, students make conjectures from a set of examples and nonexamples, and justify or refine these claims by reasoning inductively using the tools studied in unit one, which include constructions and transformations. Students learn to prove their justifications more formally by reasoning deductively and writing formal proofs. Therefore, proof should be a manifestation of student sense-making and logical reasoning —NOT a procedure.
- How do we know when two geometric figures are congruent?
- How do we prove a statement is true about parallel lines, triangles, quadrilaterals, and other polygons?