**Practice 3 (Geometric Structures) Quadrilaterals**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk/__

__Geometric Structures__

1. One can classify quadrilaterals from various perspectives:

a. Number of sides of equal length

b. Number of angles of equal measure

c. Number of pairs of sides which are parallel

d. Number of right angles

e. Whether or not the "diagonals" of the quadrilateral are perpendicular.

f. Whether or not the quadrilateral is self-intersecting.

g. Whether or not the quadrilateral's "interior" is convex.

h. Is the quadrilateral equiangular?

i. Is the quadrilateral equilateral?

j. If the quadrilateral is convex do the diagonals bisect each other?

(Definition: A set X is *convex* if for any points p and q in X the line segment joining p and q is also in X.) (Intuitively: A set is convex if it has no holes are notches.)

For each of the 4-gons below, address issues a. - j. above for that quadrilateral.

2. Can a quadrilateral have exactly 2 right angles?

3. Can a quadrilateral have exactly 3 right angles?

4. Can a self-intersecting quadrilateral be equilateral?

5. Can a self-intersecting quadrilateral be equiangular?

6. What names are commonly used to describe different kinds of quadrilaterals?