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Warm Up A Rhombus is… • A parallelogram • With all 4 sides congruent. A Rectangle is… • A parallelogram with • 4 right angles. A Square is…. • A parallelogram with… • 4 congruent sides… • And 4 congruent angles. Explore some of the properties and attributes of Rhombuses, Rectangles & Squares… • Classzone.com for more examples The diagram shows the relationships between parallelograms, rhombuses, rectangles, and squares. • • • • • All quadrilaterals All Parallelograms All Rhombuses All Rectangles All Squares Quadrilaterals Parallelograms Rectangles Rhombus SQ Corollaries about Special Quadrilaterals (p 348) • Rhombus : A quadrilateral is a rhombus iff it has four congruent sides. • Rectangle: A quadrilateral is a rectangle iff it has four right angles. • Square: A quadrilateral is a square iff it is a rhombus and a rectangle. Theorems (p 349) • Theorem 6.11: A parallelogram is a rhombus iff its diagonals are perpendicular. • Theorem 6.12: A parallelogram is a rhombus iff each diagonal bisects a pair of opposite angles. • Theorem 6.13: A parallelogram is a rectangle iff its diagonals are congruent. • A Rhombus is equilateral. • The Diagonals of a rectangle are perpendicular. • The opposite angles of a rhombus are supplementary. • A square is a rectangle. • The diagonals of a rectangle bisect each other. • The consecutive angles of a square are supplementary. Quadrilateral ABCD is a Rhombus Classwork/Homework