Explain what the "drag test" is and explain how you've used it to verify that you've constructed your figure correctly.

Construct the height h of the trapezoid through E (e.g., the perpendicular to TR and PA). Label the height of triangle PEA [math]h_1[/math] and the height of triangle TER [math]h_2[/math]. What can you say about the ratio [math]\frac{h_1}{h_2}[/math] in terms of a, b, c, or d? [br]

Write the area of the trapezoid in terms of [math]h_1[/math] and [math]h_2[/math].

Use your responses above to explain why triangle PET and triangle EAR must have the same area.

Find a primitive Pythagorean triple with hypotenuse 73. Explain how you are using your knowledge of complex numbers to find the primitive triple.

Suppose that x can be written as the sum of two squares, and y can be written as the sum of two squares.  Prove that xy can be [i]also [/i]be written as the sum of two squares.  Hint: how can you use complex numbers to write the sum of two squares as a product?[br][br][br]

Use polynomial division to find the equation of a [b][i][color=#ff0000]parabola[/color][/i][/b] that is tangent to the function [math]f\left(x\right)=x^4-2x^3+3[/math] at [math]x=1[/math] and [math]x=0[/math] . [br]