The "properties of the quadrilaterals" is a fascinating topic. In most high school classes, the students must learn the definitions and properties of the parallelogram, rhombus, rectangle, square and kite. The students may, however, find it a daunting task to remember all of the many properties, particularly if they are asked to simply memorize them. The more hands-on experience they can get, the more likely it is that they will be not only be able to remember them, but more importantly, to understand the properties.
Ideally, the exploration of the properties of the quadrilaterals would be explored in a variety of ways: via their symmetry properties in a hands-on project such as this one, using the Geometer’s Sketchpad software in either guided or open exploration, reading or writing proofs of the properties, and applying the properties through written worksheets and text homework.
Students can explore the properties of the quadrilaterals in a number of different ways. One way for students to study them is to explore their symmetries. The types of symmetries are very closely related to the theorems about the properties of the parallelogram, rectangle, rhombus, square and kite. When students create their own poster, with interactive quadrilaterals such as these, it helps them to visualize, understand, and remember the unique properties of each quadrilateral.
In this project, the quadrilateral's properties are approached via a hands-on experience with the symmetries of each. Understanding the symmetries of each quadrilateral will make the properties of each quadrilateral quite clear. For example, if a student cuts a rhombus out of paper and then folds it, he or she can intuitively experience all of the properties of the rhombus. Folding the rhombus across either diagonal shows us that the 2 "halves" of the rhombus are congruent in both directions of folding, and therefore each diagonal bisects the angles.
When the student folds a parallelogram across a diagonal, he or she can see that the 2 "halves" of the parallelogram do not match up; therefore the diagonals do not bisect the angles. All of the other properties of the quadrilaterals can also be demonstrated in this hands-on, interactive way, using reflection and rotation. The figures below provide paper patterns that students can use to experiment with the quadrilaterals by folding:
These projects can be used as interactive posters in the classroom, and students will enjoy rotating and reflecting the quadrilaterals on these posters. The hands-on experience they have making their own projects is very valuable, whether done in groups or individually. Their pride of accomplishment builds confidence and a positive attitude as well!
