Using Sketchpad to construct complementary angles (see figure).[1] Construct perfectly ho...

Using Sketchpad to construct complementary angles (see figure).

[1] Construct perfectly horizontal and perfectly vertical segments and and locate D any point inside ∠BAC. (If you have trouble, just rotate 90° about A.)

[2] Display angle measures x = m∠DAB and y = m∠CAD on the screen. (Does this sum equal 90°?)

[3] Construct any segment elsewhere on the screen.

[4] Construct an angle of measure x at E, as follows: (1) Double click on E making it a center for rotation. (2) Select x and choose Mark Angle Measurement under TRANSFORM. (3) Select segment and rotate x de-grees in a counterclockwise direction. (Move point D and observe the effect on the segment you just constructed.)

[5] Construct an angle at F having measure -y, following the procedure in Step 4. (In order to display -y on the screen for selection, choose Calculate under MEASURE and compute (- 1) y; double-click on F to make it the center of rotation.)

[6] Select the point of intersection G of the two rotated images of segment ,

(a) Drag D and see what happens to point G.

(b) Trace point G (under DISPLAY) and again move point D. What curve seems to emerge? Does your knowledge of Euclidean geometry to this point enable you to explain this phenomenon?