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Mathematics Geometry StandardMAFS.912.G-CO.3.11 Standard(s): MAFS.912.G-CO.3.11: Prove theorems about parallelograms; use theorems about parallelograms to solve problems. 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. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning Assessment Limits: • • • • • • Items may require the student to be familiar with similarities and differences between types of parallelograms (eg. squares and rectangles). Items may require the student to identify a specific parallelogram. Items may assess theorems and their converses for opposite sides of a parallelogram, opposite angles of a parallelogram, diagonals of a parallelogram, and consecutive angles of a parallelogram. Items may assess theorems and their converses for rectangles and rhombuses. Items may include narrative proofs, flow-chart proofs, two-column proofs, or informal proofs. In items that require the student to justify, the student should not be required to recall from memory the formal name of a theorem. 4 The student will be able to: • Create proofs to show the diagonals of a parallelogram bisect each other when given statements and reasons. • Prove that rectangles and rhombuses are also parallelograms when given statements and reasons. 3 The student will be able to: • • • • • Prove theorems about parallelograms with no more than two steps in a proof that the opposite sides are congruent. Prove theorems about parallelograms with no more than two steps in a proof that the opposite angles are congruent. Prove theorems about parallelograms with no more than two steps in a proof that the diagonals bisect each other. Prove theorems about parallelograms with no more than two steps in a proof that the rectangle is also a parallelogram with congruent diagonals. Solve problems with theorems about parallelograms by using algebra. 2 The student will be able to: • Use properties of parallelograms to find numerical values of a missing side or angle. • Use properties of parallelograms to select a true statement about a parallelogram. • Use properties of parallelograms to prove if a given figure is also a rectangle or rhombus. 1 The student will be able to recognize the meaning of: • Theorem, parallelogram, opposite sides, congruent, opposite angles, diagonals, bisect, conversely, rectangles. The student will be able to: • • • • Classify a quadrilateral as a parallelogram based on given properties. Classify a quadrilateral as a parallelogram based on given measures of sides or angles. Classify a parallelogram as a rectangle or rhombus based on given measures of sides or angles. Classify a parallelogram as a rectangle or rhombus based on given properties. Lastupdated8/11/16