Special Parallelograms

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Section 6.5
Special Parallelograms
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Rhombus- four congruent sides
Rectangle- four right angles
Square- four congruent sides and four rt angles.
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Theorem 6.12 A parallelogram is a rhombus if and
only if its diagonals are perpendicular.
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Theorem 6.13

• A parallelogram is a rhombus if and only if each
  diagonal bisects a pair of opposite angles.

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Theorem 6.14
A parallelogram is a rectangle if and only if its
diagonals are congruent.
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Theorem 6.15

• A quadrilateral is a rhombus if and only if it
  has four congruent sides.

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Theorem 6.16

• A quadrilateral is a rectangle if and only if it
  has four right angles.

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Guided Practice

• Decide whether the statement is true or false,
  then write the converse and state if that is true
  or false.
• 1. If a quadrilateral is a rectangle, then it is
  a parallelogram.
• 2. If a quadrilateral is a rectangle, then it is
  a rhombus.

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3. If a quadrilateral is a square, then it is a
rhombus.4. If a quadrilateral is a square, then
it is a parallelogram. 5. If a parallelogram is
a rectangle, then it is a rhombus. 6. If a
rhombus is a square, then it is a rectangle.
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Name which quadrilaterals have the property.

• a) Parallelogram b) Rectangle c) Rhombus d)
  Square

7. All sides congruent 8.
All angles are congruent 9. All
diagonals are congruent 10. Opposite
angles congruent 11. It is equiangular
and equilateral 12. The diagonals are
perpendicular