6.4 Special Parallelograms

Essential Questions: 1)How do you use properties of diagonals of

rhombuses and rectangles?2)How do you determine whether a parallelogram is a

rhombus or rectangle?

• 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.

• 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.

• 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.

Practice

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

• 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?

Practice

Practice

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

Summary

• Answer the essential questions in detailed, complete sentences.

1)How do you use properties of diagonals of rhombuses and rectangles?

2)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.