Lauretta J. Fox
Another very familiar polygon used in architecture is the quadrilateral. Ceilings, floors, walls, windows and doors usually are quadrilaterals. A
quadrilateral
is a polygon with four sides. The most common quadrilaterals are the parallelogram, rectangle, square, rhombus, and trapezoid.
A
parallelogram
is a quadrilateral whose opposite sides are parallel. The symbol used to denote a parallelogram is . A
rhombus
is an equilateral parallelogram. A
rectangle
is a parallelogram with right angles. A
square
is an equilateral rectangle.
Parallelogram

Rhombus

Rectangle

Square

(figure available in print form)
A
trapezoid
is a quadrilateral with exactly two parallel sides. The parallel sides of the trapezoid are called the
bases
. The nonparallel sides are called the legs of the trapezoid. If the legs are equal, the trapezoid is isosceles. A line segment drawn perpendicular to the bases is an
altitude
of the trapezoid. The line segment Joining the midpoints of the legs is the
median
. The length of the median is equal to one half the sum of the bases.
(figure available in print form)
ABCD is a trapezoid.
AB and DC are the bases of the trapezoid.
AD and BC are the legs of the trapezoid.
DE is an altitude of the trapezoid.
MN is a median of the trapezoid.
Suggested Assignment: Make a bulletin board to display pictures of buildings cut out of magazines. Identity all the geometric shapes that you see in the pictures. Describe how geometric shapes are used as ornaments as well as parts of structural designs in architecture.
Exercises

1.) Identify the following figures:

(figure available in print form)

2.) ABCD is a parallelogram.

(a) The sum of the angles of ’ ABC is ___ degrees.

(b) The sum of the angles of ’ ADC is ___ degrees.

(c) The sum of the angles of ’ ABCD is ___ degrees.

3.) Measure the opposite sides of ABCD. The opposite sides of a parallelogram are ___.

4.) Measure the opposite angles of ABCD. The opposite angles of a parallelogram are ___.

5.) In parallelogram ABCD draw diagonals AC and BD intersecting at X. Measure DX, XB, AX, and XC. DX and XB are ___. AX and XC are ___. The diagonals of a parallelogram ____ each other.

6.) Measure the diagonals of rectangle EFGH. The diagonals of a rectangle are ___.

7.) The bases of trapezoid QRST are 17” and 23” respectively. The length of the median of QRST is ___.

8.) Draw an isosceles trapezoid. Measure the base angles of the trapezoid. The base angles of an isosceles trapezoid are ___.

9.) Draw the diagonals of rhombus EFGH. Measure the angles formed by the intersection of the diagonals. The diagonals of a rhombus are ___ to each other.

10.) Name the polygons illustrated in the adjacent sketch. What quadrilaterals do you see in the picture?
(figure available in print form)