**Instructional Implications**If necessary, review the definition of each of the rigid motions: translations, reflections, and rotations. To develop an intuitive understanding of rigid transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites. Be sure the student understands not only how to perform a rigid motion but how to describe it using correct terminology and notation.
Review the definition of congruence in terms of rigid motion. Explain that this definition requires that a sequence of rigid motions be described that demonstrates how one of the triangles can be mapped to the other triangle in order to show they are congruent.
Have the student trace on patty paper or a transparency. Ask the student to use the transparency to model a sequence of rigid motions that maps onto providing assistance as needed. Allow the student to experiment with a variety of rigid motions. Once the student has successfully identified a sequence of rigid motions, assist the student in describing the sequence using correct terminology and notation. Provide the student with several other examples of congruent triangles and have the student first model the rigid motions that map one triangle onto the other and then describe them.
Explain to the student that this task is a part of the proof of the statement, “Two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.” Explain that when proving a statement of the form “*p* if and only if *q*” there are actually two statements that must be established: “If *p* then *q*” and “If *q* then *p*.” Consequently, to prove the statement, “Two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent,” one must prove both of the following: “If two triangles are congruent, then corresponding pairs of sides and corresponding pairs of angles are congruent,” and “If, given two triangles, corresponding pairs of sides and corresponding pairs of angles are congruent, then the two triangles are congruent.” The problem in this task is addressing the latter statement.
Consider implementing MFAS task *Congruence Implies Congruent Corresponding Parts* (G-CO.2.7), which addresses the former statement in the paragraph above.
Consider implementing MFAS task S*howing Congruence Using Corresponding Parts - 1 *(G-CO.2.7) which addresses the proof of the statement, “If all corresponding pairs of sides and all corresponding pairs of angles of two triangles are congruent, then the two triangles are congruent.” |