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Chapter 6 Lesson 4

Chapter 6 Lesson 4. Objective: To use properties of diagonals of rhombuses and rectangles. Rhombuses. Theorem 6-9 Each diagonal of a rhombus bisects two angles of the rhombus. Theorem 6-10   The diagonals of a rhombus are perpendicular. Example 1: Finding Angle Measures.

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Chapter 6 Lesson 4

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  1. Chapter 6 Lesson 4 Objective: To use properties of diagonals of rhombuses and rectangles.

  2. Rhombuses

  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 mN = 120. Find the measures of the numbered angles. Isosceles∆ Theorem ∆ Angle-Sum Theorem

  6. Example 2: Finding Angle Measures Find the measures of the numbered angles in the rhombus. Theorem 6-10 Theorem 6-9 Theorem 6-9

  7. Rectangles

  8. Theorem 6-11 The diagonals of a rectangle are congruent.

  9. Example 3: Finding the Lengths of Diagonals Find the length of the diagonals of rectangle GFED if FD = 2y + 4 and GE = 6y − 5. Theorem 6-11

  10. Example 4: Finding the Lengths of Diagonals Find the length of the diagonals of GFED if FD= 5y – 9 and GE=y + 5. Theorem 6-11

  11. Is the parallelogram a rhombus or a rectangle?

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

  13. Example 5: Recognizing Special Parallelograms Determine whether the quadrilateral can be a parallelogram. If not, write impossible.

  14. Example 6: Recognizing Special Parallelograms A diagonal of a parallelogram bisects two angles of the parallelogram. Is it possible for the parallelogram to have sides of length 5, 6, 5, and 6? No; if one diagonal bisects two angles, then the figure is a rhombus and cannot have two non-congruent sides.

  15. Assignment

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