Challenge Problem Set 2: Special Quadrilaterals

Challenge Problem Set 2: Special Quadrilaterals

For this challenge problem, you will submit work in paper form. Work may be done on a computer or by hand. We strongly advise you to make a back up of your work either by keeping any computer files generated or by taking an image of your work with a scanner, tablet or phone and saving the image. The work you genearate will be a good reference when preparing for cumulative exams in the future.

Collaboration rules

·  You are to work independently for the entirety of this challenge problem.

·  Any evidence of collaboration would be an LHS Honor Code violation with serious consequences forboth students. You should be aware that the Math 2 teachers work together to detect illegal sharing between students who have different teachers.

·  You may ask your teacher for help.

Create a venn diagram of special quadrilaterals:

Your study of special quadrilaterals will consist of discovering and/or proving many properties of each quardilateral. Your task is to graphically resepresent the relationship between them all in one large venn diagram. All quadrilaterals should be represented and there should only be regions in your diagram that contain elements. To explain this first we present the following examples that relate to the study of triangles…

Note that the Equilateral triangles are entirely within the isosceles triangles. This indicates, correctly, that all equilateral triangles are also isosceles.

In the second example we see that Isosceles triangles have been correctly separated from the Scalene. However, there is a region (see arrow) within Triangles that is neither Isosceles nor Scalene. Since no such triangles exist, this is a minor error.

Here we see Right Triangles and Isosceles Triangle presented as disjoint sets (no overlap). This implies that there are no Right Triangles that are Isosceles. This is simply not true, so this too is a major error.

Your turn:

Begin with a large region of quadrilaterals. Your diagram should accurately show overlapping (or not!) regions for: Quadrilaterals, Isosceles Trapezoids, Kites, Parallelograms, Rhombi, Rectangles, Squares, and Trapezoids.

Quality of presentation is an important aspect of your submitted work. While we do not expect, (nor will it improve your grade to do so) you to “decorate” your work, neatness and clarity do count. It is not advisable to submit your first draft.

Due Date: ______

Except for an excused absence or extenuating circumstances, late challenge problems will not be accepted.

Challenge Problem 2 will be graded as a quiz grade (3/12) for Quarter 1.