Rhombi and Squares

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Rhombi and Squares

• Section 6.5

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Rhombus or plural is Rhombi

• A quadrilateral with all 4 sides congruent
• Properties
• 1. Diagonals are perpendicular
• 2. Each diagonal bisects a pair of opposite
  angles

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Square

• A quadrilateral with four right angles and four
  congruent sides
• Properties
• 1. All properties of parallelograms apply
• AND
• 2. All properties of rectangle apply
• AND
• 3. All properties of a rhombus apply

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Examples

• ABCD is a rhombus
• 1. If m ltABD 60,
• Find mltDBC.
• ANS 60
• 2. If AE 8, find AC.
• ANS 16
• 3. If AB 26 and BD 20, find AE.
• ANS 24

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• 4. Find mltCEB.
• ANS 90
• 5. If mltCBD 58,
• Find mltACB.
• ANS 32
• 6. If AE 3x 1 and AC 16, find x
• ANS 3
• 7. If mltCDB 6y and mltACB 2y 10, find y.
• ANS 10

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If given four ordered pairs and asked to decide
what shape the quadrilateral is

• 1. Check the slope of the opposite sides to see
  if it is a parallelogram.
• 2. If it is a parallelogram check the slope of
  the consecutive sides to see if it is a
  rectangle.
• 3. If the sides are perpendicular, then it may
  be a square or rectangle so check the side
  lengths.

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• 4. If all four sides are congruent it is a
  square, if only the 2 pairs of opposite sides are
  congruent then it is a rectangle.
• 5. If sides are parallel but no right angles, it
  must be a rhombus.

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• Determine whether the given vertices represent a
  parallelogram, rectangle, rhombus, or square.
  Explain
• A(1, 3) B(7, -3) C(1, -9) D(-5, -3)
• Step 1 Graph the ordered pairs.
• Step 2 Find the slope of all four sides
• Step 3 Find the length of all four sides.