Download - 6.4 Special Parallelograms
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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?
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• 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.
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• 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.
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• 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.
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Practice
• Find the length of the diagonals of rectangle GFED if FD = 5y – 9 and GE = y + 5.
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• 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?
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Practice
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Practice
• A parallelogram has angles of 30°, 150°, 30°, and 150°. Can you conclude that it is a rhombus or a rectangle? Explain.
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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.