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Definitions, theorems, and corollaries for rhombuses, rectangles, and squares, as well as ways to identify parallelograms. It includes exercises to determine if given quadrilaterals are parallelograms based on their properties.
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Special Parallelograms Definitions Name Definition Picture Rhombus Rectangle Square Theorems and Corollaries Name Theorem/Corollary Picture Rhombus Corollary A quadrilateral is a rhombus if and only if Rectangle Corollary A quadrilateral is a rectangle if and only if Square Corollary A quadrilateral is a square if and only if Perpendicular Diagonals Theorem A parallelogram is a rhombus if and only if Bisecting Diagonals Theorem A parallelogram is a rhombus if and only if Congruent Diagonals Theorem A parallelogram is a rectangle if and only if
Ways to Prove a Quadrilateral is a Parallelogram Use the information in the diagram above to answer the following questions.
Review
Special Parallelograms Parallelogram Rectangle Rhombus Square Trapezoid Sketch Properties 1 Both pair of opposite sides || 2 Both pair of consecutive sides ⊥ 3 Diagonals are ≅ 4 Diagonals are ⊥ 5 Diagonals bisect each other 6 Both diagonals are angle bisectors 7 All sides are ≅ 8 Exactly one pair of opposite sides are || 9 All angels are 90° 10 Both pair of opposite angles are ≅ 11 Consecutive angles are supplementary Examples: Name each quadrilateral – parallelogram, rectangle, rhombus, and square – for which the statement is true.