Download MAFS.912.G-CO.3.11: Prove theorems about parallelogram

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:
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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.
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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.
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The student will be able to:
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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.
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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.
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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:
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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