 ## The Satisfaction of a Job Well Done

A few days ago, I got a call from my uncle, Jerry, asking me if I could tutor his daughter, my cousin, Tayler.  Of course I agreed!  According to my uncle, my cousin was feeling very frustrated with the material in the classroom and more at home trying to understand.  So frustrated nearly to the point of tears.  So she took some time to cool off and clear her head for about an hour. I put this flowchart together years ago to help our students become familiar and identify quadrilaterals and their properties using side lengths and the slopes of the sides.  The information is usually gathered from a gridded Cartesian graph or sets of ordered pair vertices of the quadrilateral.

#### Information Needed or to be Derived:

Points: $(x_1, y_1) \text{ and } (x_2, y_2)$

Pythagorean Theorem: $\displaystyle c^2 = a^2 + b^2$ $\displaystyle \text{side length}=\sqrt{(\Delta x)^{2}+(\Delta y)^{2}}$ $\displaystyle \text{side length} = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Slope: $m=\frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}$