Quadrilaterals - Definitions and Constructions
- Tibor Marcinek
As discussed in our class, there are many ways to construct a given quadrilateral. Constructions differ in their "underlying" minimal definitions that guide the process of construction. As teachers, you should be able to analyze constructions to reveal definitions and the other way around - be able to construct quadrilaterals based on given definitions. These problems can be challenging. Please keep in mind that the point of these activities in not to memorize definitions or construction steps; Quite the opposite. It is to see that the same object can be defined in many different ways, and that by engaging in class discussions of different ideas, we can start to see the conditons that are necessary and sufficient to define an object. For students who are ready to step up from the Van Hiele's Informal to Formal Deduction level (typically around high school age), it is often more beneficial to "learn to define" and understand what makes a good definition, rather than to "learn definitions". This also taps well to CCSS for Mathematical Practice (http://www.corestandards.org/Math/Practice/). Before attempting these tasks, make sure you know what makes a good construction - the one that is not under- nor overconstrained (see our previous activities). And if you find an error somewhere, bring it up, too (for bonus points!).