6-4 S PECIAL P ARALLELOGRAMS M11.C.1 2.9.11.C Objectives: 1) To use properties of diagonals of rhombuses and rectangles 2) To determine whether a parallelogram.

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6-4 S PECIAL P ARALLELOGRAMS M11.C C Objectives: 1) To use properties of diagonals of rhombuses and rectangles 2) To determine whether a parallelogram is a rhombus or a rectangle

T HEOREMS Each diagonal of a rhombus bisects two angles of the rhombus The diagonals of a rhombus are perpendicular.

E XAMPLE : F INDING A NGLE M EASURES MNOP is a rhombus. Angle N is 120. Find the measure of the numbered angles

E XAMPLE : P AGE 313 Find the measure of the numbered angles.

THEOREM The diagonals of a rectangle are congruent.

E XAMPLE : F INDING D IAGONAL L ENGTH Rectangle ABCD BD = 2y + 4 AC = 6y - 5

T HEOREMS If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

R ECOGNIZING S PECIAL P ARALLELOGRAMS Determine whether the quadrilateral can be a parallelogram. If not, write impossible. 1. The quadrilateral has congruent diagonals and one angle of 60 degrees. 2. The quadrilateral has perpendicular diagonals and four right angles. 3. A diagonal of a parallelogram bisects two angles of the parallelogram. Is it possible for the parallelogram to have sides of lengths 5, 6, 5, and 6? Explain.

Homework Page 315 #1-21