Lesson #13 - Parallelograms

New Lesson - July 27, 2012
Revision date - Fall 2017

Purpose: This lesson introduces the definitions and properties of parallelograms. The Logo program provides an excellent environment to explore different types of parallelograms. This lesson uses a procedure with three variables to efficiently draw a given parallelogram. This lesson contains optional information on how to set the dimensions of the graphic window.
Essential Question: Can you apply your knowledge of interior and exterior angle measures to code and investigate the properties of parallelograms?

A Section of the Lesson Follows

A quadrilateral is a closed polygon with exactly four sides.
A parallelogram is a quadrilateral that has two pairs of parallel sides.
A rectangle is a parallelogram with a right angle.
A square is a rectangle with all sides of equal length (equilateral).
A rhombus is a parallelogram with all sides of equal length (equilateral).
Recall that a regular polygon is both equiangular and equilateral. The square (introduced in Lesson #5) is the only regular quadrilateral.
*Note that the precise wording of a definition will vary depending on the book you are using. For example, a square could be defined as a rhombus with a right angle.

The graphic in Figure 13.1 shows parallelogram ABCD with given side lengths of 135 pixels by 195 pixels and an acute interior angle of 40 degrees. An auxiliary line was drawn from point A perpendicular to line BC. Write and test the Logo code for this shape starting at point A. (check your work at the end of this lesson).

Open the editor and name the new procedure PARA (as shown in figure 13.4).
Type X Y A for the input variables
Enter REPEAT 2[FD X RT (180-A) FD Y RT A) in the command window
Define (save) the procedure

Run the procedure from the listener window by typing para 80 50 90 without any brackets. This is the code for the first rectangle in figure 13.3. Note that when you run the procedure from the listener window you must type three values after the PARA command.

*Note that this lesson includes a Venn diagram and T/F questions with regard to quadrilaterals.
*This lesson includes the AIA Theorem.