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6-4 Special Parallelograms M11.C.1 2.9.11.C

6-4 Special Parallelograms M11.C.1 2.9.11.C. Objectives: To use properties of diagonals of rhombuses and rectangles To determine whether a parallelogram is a rhombus or a rectangle. Theorems. Each diagonal of a rhombus bisects two angles of the rhombus.

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6-4 Special Parallelograms M11.C.1 2.9.11.C

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  1. 6-4 Special ParallelogramsM11.C.1 2.9.11.C Objectives: To use properties of diagonals of rhombuses and rectangles To determine whether a parallelogram is a rhombus or a rectangle

  2. Theorems • Each diagonal of a rhombus bisects two angles of the rhombus • The diagonals of a rhombus are perpendicular.

  3. Example: Finding Angle Measures • MNOP is a rhombus. • Angle N is 120. • Find the measure of the numbered angles

  4. Example: Page 313 • Find the measure of the numbered angles.

  5. THEOREM • The diagonals of a rectangle are congruent.

  6. Example: Finding Diagonal Length Rectangle ABCD BD = 2y + 4 AC = 6y - 5

  7. Theorems • 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.

  8. Recognizing Special Parallelograms • Determine whether the quadrilateral can be a parallelogram. If not, write impossible. • The quadrilateral has congruent diagonals and one angle of 60 degrees. • The quadrilateral has perpendicular diagonals and four right angles. • 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.

  9. Homework • Page 315 #1-21

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