6.4 Special Parallelograms

1. 6.4 Special Parallelograms Essential Questions: How do you use properties of diagonals of rhombuses and rectangles? How do you determine whether a parallelogram is a rhombus or rectangle?

2. Theorem 6-9 • Each diagonal of a rhombus bisects two angles of the rhombus. • Proof on page 329 • The diagonals of a rhombus provide an interesting application of the Converse of the Perpendicular Bisector Theorem.

3. Theorem 6-10 • The diagonals of a rhombus are perpendicular. • This is due to the Converse of the Perpendicular Bisector theorem. • You can use Theorems 6-9 & 6-10 to find angle measures in rhombuses.

4. Theorem 6-11 • The diagonals of a rectangle are congruent. • Proof on page 330. • Theorems 6-9, 6-10, & 6-11 all deal with the diagonals of rectangles and rhombuses.

5. Practice • Find the length of the diagonals of rectangle GFED if FD = 5y – 9 and GE = y + 5.

6. 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. • What are these converses of?

7. Practice

8. Practice • A parallelogram has angles of 30°, 150°, 30°, and 150°. Can you conclude that it is a rhombus or a rectangle? Explain.

9. Summary • Answer the essential questions in detailed, complete sentences. • How do you use properties of diagonals of rhombuses and rectangles? • How do you determine whether a parallelogram is a rhombus or rectangle? • Write 2-4 study questions in the left column to correspond with the notes.