1 / 16

6 – 4 Special Parallelograms

6 – 4 Special Parallelograms. L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a parallelogram is a rhombus or a rectangle?. Theorem 6 – 9: Rhombus Diagonals Bisect Angles. Each diagonal of a rhombus bisects two angles of the rhombus.

payton
Télécharger la présentation

6 – 4 Special Parallelograms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6 – 4 Special Parallelograms L.E.Q. How do you use properties of diagonals of rhombuses and rectangles and determine whether a parallelogram is a rhombus or a rectangle?

  2. Theorem 6 – 9: Rhombus Diagonals Bisect Angles. • Each diagonal of a rhombus bisects two angles of the rhombus.

  3. Theorem 6 – 10: Rhombus Diagonals are Perpendicular. • The diagonals of a rhombus are perpendicular.

  4. Example 1: Finding Angle Measures. • MNPQ is a rhombus and • Find the measure of the numbered angles.

  5. Find the measures of the numbered angles in the rhombus below.

  6. Theorem 6 – 11: Diagonals of a Rectangle. • The diagonals of a rectangle are congruent.

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

  8. Find the length of the diagonals of GFED if FD = 5y - 9 and GE = y + 5.

  9. Theorems Used to Prove Whether a Parallelogram is a Rhombus or a Rectangle.

  10. Theorem 6 – 12: • If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.

  11. Theorem 6 – 13: • If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

  12. Theorem 6 – 14: • If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

  13. Example 3: Recognizing Special Parallelograms. • Determine whether the quadrilateral can be a parallelogram. If not, write impossible. Explain. • The quadrilateral has congruent diagonals and one angle of 60 degrees. • The quadrilateral has perpendicular diagonals and four right angles.

  14. 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.

  15. Example 4: Real-World Connection. • Community Service Builders use properties of diagonals to “square up” rectangular shapes like building frames and playing-field boundaries. Suppose you are on the volunteer building team at the right. You are helping to lay out a rectangular patio. Explain how to use properties of diagonals to locate the four corners.

  16. Homework: • Pgs. 315-317 #s 2 – 20 even, 48 – 50 all.

More Related