Quadrilaterals

Here is a place to offer your version of a definition for a quadrilateral. Let's try to agree on one.

Quadrilateral: Given 3 non collinear points, A,B,C, a quadrilateral is the union of the segments AB,BC,CD,AD such that D is in the interior of angle ABC, or D is in the interior of the vertical angle to angle ABC.

Given four distinct points A, B, C, and D (where no three are collinear), a quadrilateral is the union of four of the segments AB, AD, AC, BC, BD, CD such that each segment intersects with exactly one other segment at each endpoint.

(Bob) Given four distinct points A, B, C, and D, such that A, B are on the same side of the line containing C and D; A, D are on the same side of the line containing B and C; a quadrilateral is the union of the segments AB, BC, CD, and AD.

Brett's Definition (revised): Given any 2 distinct points A,C, let the points B,D be any distinct points such that B,D are on opposite sides of the line AC and that no three points are colinear. The union of the segemnts AB, BC, CD,and DA is a quadrilateral. (I had a typo that has been fixed).

(Lisa) As I drew pictures for each of the above definitions, I liked Bob's definition the best. I agree with the first definition, but we have to rely on the definition of vertical angles in order to effectively use this. It may not be the most concise definition. In Brett's definition, I don't think B and D have to be on opposite sides of line AC. If, as is stated in the first definition, D is in the interior of the vertical angle to ABC, then B and D are on the same side of line AB, but a quadrilateral is still constructed.