Special Parallelograms

1
Special Parallelograms

• A double-edged straightedge has two parallel
  sides
• Draw line segments along both sides of the
  straightedge
• Move the straightedge so it crosses both lines
  and repeat
• What figure is produced by the intersecting
  lines?
• So you can draw a rhombus by tracing both edges
  of a straightedge
• You can draw a parallelogram by using two
  straightedges with different widths.
• C-49 Double-edged Straightedge Conjecture
• If two sets of parallel lines that are the same
  distance apart cross, they create a rhombus.

2
Special Parallelograms

• Draw both diagonals of your rhombus
• You (should) already know the diagonals bisect
  each other
• Do you see anything else special about the
  diagonals themselves?
• Is there anything special about the diagonals and
  the vertex angles?
• C-50 Rhombus Diagonals Conjecture
• The diagonals of a rhombus are perpendicular
  bisectors of each other.
• C-51 Rhombus Angles Conjecture
• The diagonals of a rhombus bisect the angles of
  the rhombus.

3
Special Parallelograms

• Draw a rectangle and both of its diagonals
• Since a rectangle is an equiangular
  parallelogram, the diagonals bisect each other
• Do you see anything else special about the
  diagonals?
• C-52 Rectangle Diagonals Conjecture
• The diagonals of a rectangle are congruent and
  bisect each other.
• Draw a square and both of its diagonals
• A square can be considered to be an equiangular
  rhombus or an equilateral rectangle. What about
  the diagonals?
• C-53 Square Diagonals Conjecture
• The diagonals of a square are congruent and
  perpendicular bisectors of each other.