6.5 Rhombi and Squares

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6.5 Rhombi and Squares
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Rhombus

• Quad with 4 ? sides

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Rhombus

• Theorem 6.15 The diagonals of a rhombus are ? .
• Theorem 6.16 If the diagonals of a
  parallelogram are ?, then the parallelogram is a
  rhombus.
• Theorem 6.17 Each diagonal of a rhombus bisects
  a pair of opposite angles.
• All 4 of the ?s are ?.

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Example

• Refer to Example 2 picture on page 349
• Do Check Your Progress 2
• Answer
• 114

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Square

• Both a rhombus and a rectangle
• All sides are ?
• All angles are right angles (90)

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Example

• Given the vertices J(5,0), K(8, -11), L (-3,-14),
  M(-6,-3), determine whether parallelogram JKLM is
  a rhombus, a rectangle, or a square. List all
  that apply.
• Use the distance formula to compare the lengths
  of the diagonals. Use the slope formula to
  determine if the sides are perpendicular.
• Answer Square, rectangle, and rhombus, all
  sides are congruent and perpendicular.

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Summaries

• Rhombus Properties
• Opposites sides are ?
• Opposite angles are ?
• Consecutive angles are supplementary.
• Diagonals bisect each other
• Diagonals are perpendicular
• Each diagonal bisects two angles.
• 4 sides are ?

• Square Properties
• Opposites sides are ?
• Opposite angles are ?
• Consecutive angles are supplementary.
• Diagonals bisect each other
• Diagonals are perpendicular
• Each diagonal bisects two angles.
• All four angles are right angles.
• Diagonals are ?
• 4 sides are ?

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Homework 41

• p. 352 11, 15-18, 19-25 odd, 31-34