Trapezoid Median (Midsegment) Action!

Interact with the applet below for a few minutes. Then, answer the questions that follow. Be sure to change the locations of the white points each time before re-sliding the slider!


How do you know the quadrilateral initially constructed is a trapezoid? (What postulate or theorem helps justify this?)


The thick black segment (with three tick marks) is called a median (or midsegment) of a trapezoid. Define the term median of a trapezoid without looking up its definition on another site.


What two facts/properties about the median of a trapezoid does this applet illustrate?


Suppose the bases of the trapezoid above measured 14 inches and 26 inches. What would the length of its median be?


Suppose a trapezoid has a median with length 35 inches and one base measuring 23 inches. What would the length of its other base be?


Now move any point so that one of the trapezoid's bases has length = 0. Then re-slide the slider. What other theorem(s) previously learned does this applet now show?


Prove each of these 2 facts (you listed in your response to question (3) above) true using the format of a 2-column, paragraph, or coordinate geometry proof.

Quick (Silent) Demo