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Warm Up

Warm Up. EC = EP = m PR = . 5. RE = 6. CP = 7. m 8. m. Section 6 – 4 Special Parallelograms. Objective: To use properties of diagonals of rhombuses and rectangles. Theorem 6 – 9 . Each diagonal of a rhombus bisects two angles of the rhombus. Theorem 6 – 10.

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Warm Up

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  1. Warm Up EC = EP = m PR = 5. RE = 6. CP = 7. m 8. m

  2. Section 6 – 4 Special Parallelograms Objective: To use properties of diagonals of rhombuses and rectangles

  3. Theorem 6 – 9 Each diagonal of a rhombus bisects two angles of the rhombus.

  4. Theorem 6 – 10 The diagonals of a rhombus are perpendicular

  5. Example 1 Finding Angle Measures • MNPQ is a rhombus and m ∠ N = 120. Find the measures of the numbered angles.

  6. B) Find the measures of the number angles in the rhombus. C) Find the measures of the number angles in the rhombus.

  7. Homework:6 – 4 Ditto; #1, 4, 6

  8. Section 6 – 4 Continued Objectives: To use properties of diagonals of rectangles To determine whether a parallelogram is a rhombus or a rectangle.

  9. Theorem 6 – 11 The diagonals of a rectangle are congruent. FD = GE

  10. Example 2 Finding Diagonal Length A) Find the length of the diagonals of rectangle GFED if FD = 2y + 4 and GE = 6y – 5.

  11. B) ABCD is a rectangle. Find the length of the diagonal if AC = 2(x – 3) and BD = x + 5.

  12. Theorem 6 – 12 If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a Theorem 6 – 13 If the diagonals of a parallelogram are perpendicular, then the parallelogram is a Theorem 6 – 14 If the diagonals of a parallelogram are congruent, then the parallelogram is a

  13. Example 3 Recognizing Special Parallelograms Determine whether the quadrilateral can be a parallelogram. If not, write not possible. A) The quadrilateral has congruent diagonals and one angle of 60°. B) The quadrilateral has perpendicular diagonals and four right angles.

  14. A diagonal of a parallelogram bisects two angles of a parallelogram. It is possible for the parallelogram to have sides of length 5, 6, 5, and 6? • The diagonals of ABCD are perpendicular. AB=16 cm and BC=8 cm. Can ABCD be a parallelogram?

  15. In the Rhombus, find the measure of each numbered angle, then find the area of the rhombus.

  16. Homework:Finish 6 – 4 Ditto

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