Geometry, Quarter 2, Unit 2.3 Proving Theorems About Parallelograms Days: 11

Common Core State Standards for Mathematical Content Congruence G-CO Prove geometric theorems [Focus on validity of underlying reasoning while using variety of ways of writing proofs] G-CO.11Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Expressing Geometric Properties with Equations G-GPE Use coordinates to prove simple geometric theorems algebraically [Include distance formula; relate to Pythagorean theorem] G-GPE.4Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Standards of Math Practice Make sense of Problems and Persevere in Solving Them Construct Viable Arguments and Critique Reasoning of Others Attend to Precision

Essential Questions What are the similarities and differences between parallelograms and rectangles? Why are parallelograms and their properties important in our study of geometry? Why are triangle congruencies important in our study of Geometry? When are manipulatives helpful in proving a theorem?