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## 6.4:Special Parallelograms

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**6.4:Special Parallelograms**Objectives: To use the properties of diagonals of rhombuses and rectangles Determine whether a parallelogram is a rhombus or a rectangle**Review of the Properties of a parallelogram:**• 2 pairs of opposite parallel sides • 2 pairs of opposite congruent sides • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals bisect each other Special Parallelograms: Rhombus, Rectangle, Square • These figures will inherit ALL the properties above, AND they will each add their own individual properties**Theorems For a Rhombus:**• Each diagonal of a rhombus bisects 2 angles of the rhombus • The diagonals of a rhombus are perpendicular bisects & bisects & D C B A**Examples: Find the measures of the numbered angles in the**rhombus. 1 12° 2 4 3**Theorem for Rectangle**The diagonals of a rectangle are congruent. (remember, they also are bisected, so all 4 segments created by the intersection are congruent) AND E**EXAMPLE**BD=5y-7 and AC = y + 5. Find the value of y and the length of BE. E**THEOREMS**If one diagonal of a bisects 2 angles of the then the is a RHOMBUS. If the diagonals of a are perpendicular, then the is a RHOMBUS. If the diagonals of a are congruent, then the is aRECTANGLE.**SQUARE**Remember, a square is a RECTANGLE and a RHOMBUS, so it inherits ALL the properties of a rectangle, rhombus and parallelogram.**Determine whether the quadrilateral can be a parallelogram.**If not, write impossible. Explain your answer. • Each diagonal is 15 cm long, and one angle of the quadrilateral has a measure of 45°. • The diagonals are congruent, perpendicular, and they bisect each other.