Prove theorems about parallelograms

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Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
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HSG.CO.C.11

**HSG.CO.C.11**: Prove 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.

HSG.CO.C.11: Prove 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.

What you'll learn

Prove that opposite sides of a parallelogram are congruent, using triangle congruence and the properties of parallel lines
Prove that opposite angles of a parallelogram are congruent, using the properties of parallel lines and supplementary co-interior angles
Prove that the diagonals of a parallelogram bisect each other, and conversely, that if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram
Prove that rectangles are parallelograms with congruent diagonals, and conversely, that a parallelogram with congruent diagonals is a rectangle
Distinguish between properties of general parallelograms and properties specific to special parallelograms (rectangles, rhombi, squares) and apply these theorems in multi-step proofs

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Slides

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Parallelogram properties

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Rectangles and special parallelograms

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Practice

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Exercise

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