By: Tim Lehman

Before we can start any discussion on two-dimensional figures, the vocabulary to be used must be established. Definitions of shapes need to be agreed upon. These include (but are not limited to) circle, triangle, quadrilateral, trapezoid, parallelogram, rectangle, rhombus, square, pentegon, and other n-gons. Further, other terms used in later lessons such as acute, obtuse, right, scalene, isosceles, and equilateral triangle and regular should be discussed.

One method to establish the definition of the
shapes is to present to students with examples and non-examples
of a given figure. If these are chosen carefully, students can
determine the proper definitions. Here are GSP sketches of **examples** and **non-examples**
of trapezoids.

Other possible topics of exploration exist
for this lesson. Some simply clarify definitions. Are squares
always rectangles? Are rectangle always squares? The class can
also discuss (and explore on GSP) questions with some more depth
to them, such as: Can a right triangle have two right angles?
What does a circle with an infinite diameter look like? Students
may also find interesting the properties of centers of triangles
(two examples **here**
and **here**)
or examine diagonals of different quadrilaterals (compare how
diagonals intersect for rectangles, parallelograms, and squares,
for example).