6.4 Special ParallelogramsMAD GAB

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Theorem

Theorem 6.9: Each diagonal of a rhombus bisects two angles of the rhombus.

Theorem

Theorem 6.10: The diagonals of a rhombus are perpendicular.

BDAC

Applications

Find the measures of the numbered angles of the rhombuses.

TheoremTheorem 6.11: The diagonals of a rectangle are congruent.

Statements Reasons

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

7. 7.

8. 8.

ramparallelog a is ABCD

DCAB BCBC

s rt. are and DCBABC

DCBABC

DCBABC BDAC

Find the length of segment FD in rectangle GFED if FD = 3y + 4 and GE = 6y – 5.

Applications

CONVERSES…

Theorem 6.12: If one diagonal of a parallelogram bisects two angles of the parallelogram, the parallelogram is a rhombus.

Theorem 6.13: If the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus.

Theorem 6.14: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Applications

Can you conclude that the parallelogram is a rhombus or a rectangle? Explain.

6.4 Special Parallelograms

HW 6.4:1-15 odd, 16-18, 21, 25-34

Work on THT! (Due Monday!!!)

Quiz 6.1-6.3 on Friday!

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