Carry out the following experiment using Sketchpad.[1] Construct ΔABC and locate point D o...

Carry out the following experiment using Sketchpad.

[1] Construct ΔABC and locate point D on side (shown in the figure below).

[2] Construct segment , and select segments and in that order. Choose Mark Ratio from the TRANSFORM menu. (Also, display the ratio AD/AB.)

[3] Select point B for the choice Mark Center on that menu, then select point C for a dilation along segment , as follows: Choose Dilate from the TRANSFORM menu, with marked ratio checked. Point C will be mapped to C' such that BC' = BC • AD/AB.

[4] Repeat Step 3 to dilate point A along segment to A' such that

CA' = AC•AD/AB. (Thus, the ratios AD/AB, BC'/BC, and CA'/CA are equal.)

[5] Construct the segments , ,and . Obtain the points of intersection E, F, and G of these segments, and construct the interior of ΔEFG displaying its area on die screen using Polygon Interior from the CONSTRUCT menu and Area from the MEASURE menu.

Drag point D on segment . What fundamental theorem in geometry did you "discover"?