Definition: A [color=#0a971e]MEDIAN[/color] of a TRIANGLE is a segment that connects that triangle's VERTEX to the MIDPOINT of the SIDE OPPOSITE that vertex. [br]Definition: 3 or more lines are said to be CONCURRENT LINES if and only if they intersect at exactly 1 point. [br] (Their point of intersection is called the point of concurrency.) [br][br]A triangle's 3 [color=#0a971e]MEDIANS[/color] are ALWAYS concurrent. Their point of concurrency is called the [color=#0a971e]CENTROID[/color] of the triangle.[br]Did you know that the [color=#0a971e]CENTROID[/color] of a triangle its center of gravity? It is.[br][br]There is another interesting fact about a triangle's [color=#0a971e]centroid[/color] you will soon discover after interacting with the applet below. [br]The directions & investigation questions are displayed below the applet.

Questions. (BE SURE to drag/move vertices A, B, & C around during your pursuit of answers to these questions below!) [br][br]1) Is it ever possible for a triangle's [color=#0a971e]CENTROID[/color] to lie OUTSIDE the triangle? If so, under what circumstance(s) will this occur?[br]2) Is it ever possible for a triangle's [color=#0a971e]CENTROID[/color] to lie ON THE TRIANGLE ITSELF? If so, under what circumstance(s) will this occur?[br]3) If your answer for (2) was "YES", where on the triangle did point [color=#0a971e]G[/color] lie?[br]4) Is it ever possible for a triangle's [color=#0a971e]CENTROID[/color] to lie INSIDE the triangle? If so, under what circumstance(s) will this occur?[br][br]5) Click on the four checkboxes in the upper right hand corner (one after the other) to observe some pretty cool phenomena. [br]6) After clicking the "[color=#1551b5]CHECK THIS OUT !!![/color]" checkbox, be sure to answer the [color=#c51414][b]bold question that appears in red[/b][/color]. Answer it in detail, trying to explain (as best you can) the phenomena you observe.