Greenwood press

QUADRILATERALS
93
convex
square
rectangle
isosceles trapezoid
kite
parallelogram
rhombi (diamonds)
trapezoid
Different types and uses of common quadrilaterals.

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tangle and a rhombus. Hence it has only right angles, its diagonals are congruent
and perpendicular, and all four sides are of equal length.
There are many uses of parallelograms in carpentry. A four foot by six foot
window frame is made by connecting four-foot pieces to the six-foot pieces so
that opposite sides of the frame are equal in length. The resulting figure is a par-
allelogram. Even though the corners are securely connected, it is likely to shear
so that the angles are not 90 degrees. Even a slight deviation may mean that a
rectangular window will not fit into the frame. To square the frame, the carpen-
ter measures the diagonals. The parallelogram frame will be rectangular only
when the diagonals have the same length. When the frame is in the wall opening,
the carpenter will use shims, small pieces of wood, to adjust the fit of the frame
until the diagonals are the same length. Then the carpenter can be sure that the
rectangular window will fit into the frame. 
Doors are usually shaped like rectangles so that they can seal better at their
hinge, or at their edges. An entire side of a door can be well connected to a set of
hinges, as well as allow a person to easily walk through. If the door were shaped
as an oval it would be primarily for design purposes, since the door would likely
be less durable and more expensive. Only a small section could be attached to
maybe one hinge, affecting its ability to stay well connected to the house. In
addition, walking through the doorway would be more challenging, because less
floor space would be available as compared to the flat edge of a rectangle. Some-
times doorways are rectangular and have an arch at the top, which is an archi-
tectural style seen in many cultures. It is built principally for design or historical
significance and is usually more difficult and expensive to construct.
Floor tiles in the shape of the same quadrilateral will always fit perfectly,
because the sum of any quadrilateral’s angles is 360 degrees, the same measure
of degrees in a circle. In order to tessellate a plane, all of the objects must con-
nect perfectly without any gaps or overlaps—what you would expect of tiles in
a bathroom or kitchen. At the point where multiple tiles intersect, their interior
angles must equal 360 degrees so that they fit neatly around a common center
point. If the different angles of a quadrilateral are used around an intersection of
four quadrilaterals, they will always tessellate perfectly.
Trisection of a long piece of lumber into thinner strips requires that guide
lines be set up for the ripsaw. A carpenter can take a 12-inch ruler and rotate it so
that its opposite ends are at the edges of the lumber. After marking the board at
the 4 and 8 inch positions at one end, the carpenter slides the ruler down the
board and marks the 4 and 8 inch positions at the other. Corresponding marks are
used to draw long lines down the board as guides for the saw. This works,
because the marks at 4 and 8 inches provide vertices of a parallelogram.