Congruent polygons

Students will learn how rigid transformations are used to define congruence. Then students will see two proofs. The first, is that two segments are congruent if and only if they have the same length (video). The second, is that two angles are congruent if and only if they have the same measure (video). From these proofs, it's easy to see corresponding parts of congruent polygons must be congruent. Students will practice solving problems where side lengths and angles of congruent polygons are labeled with algebraic expressions. The objective for students is to find the value of some variable. They'll use the definition of congruence to make some equation, possibly multi-step, then solve as usual.