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Parallelogram. • DEFINITION: Parallelograms are quadrilaterals with both pairs of opposite sides parallel. • D • Quadrilateral. DEFINITION: Quadrilateral just means "four sides" (quad means four, lateral means side). Any four-sided shape is a Quadrilateral. But the sides have to be straight, and it has to be 2dimensional. RECTANGLES PARALLELOGRAMS QUADRILATERALS RHOMBI SQUARES 5 Things About Parallelograms DEFINITION 1) Both Pairs Opp Sides Parallel PROPERTIES 2) Both Pairs Opp Sides Congruent 3) Both Pairs Opp Angles Congruent 4) Consecutive Angles Supplementary 5) Diagonals Bisect Each Other SPECIAL CASES: • RHOMBOID – A quadrilateral whose opposite sides are parallel and adjacent sides are unequal, and whose angles are not right angles • RECTANGLE – A parallelogram with four angles of equal size • RHOMBUS – A parallelogram with four sides of equal length. • SQUARE – A parallelogram with four sides of equal length and angles of equal size (right angles). Proof of Theorem: If a quadrilateral is a parallelogram, the 2 pairs of opposite sides are congruent. STATEMENTS REASONS 1 2 Draw segment from A to C 3 1 2 3 4 4 5 5 6 6 7 7 Given Two points determine exactly one line. A parallelogram is a quadrilateral with both pairs of opposite sides parallel. If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Reflexive property: A quantity is congruent to itself. ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. CPCTC: Corresponding parts of congruent triangles are congruent.