17. Use Sketchpad to construct a triangle ∆ABC having these measurements:AB = 1.5, AC = 2,...

17. Use Sketchpad to construct a triangle ∆ABC having these measurements:

AB = 1.5, AC = 2, and m∠ACB = 30:

[1] Locate A and translate it 1.5 units horizontally to A' = B. Translate it 2 units horizontally to A".

[2] Construct Circle With Center A and Radius . (Since AB = 1.5 and = 2, then any point C on the circle will have AC = 2, as desired, but ∠ACB probably needs to be adjusted.)

[3] Locate point Con circle AA" and construct segments and , then dis-play m∠ACB on the screen. By dragging C, you can make m∠ACB = 30 (or nearly so). Accuracy to within 0.05 units will be acceptable.

(a) Did you find more than one triangle having the required measurements? If so, construct a second point D on the circle with m∠ADB = 30. (There are four positions for point P on the circle for which m∠APB = 30.)

(b) Try to find something significant about the two noncongruent triangles you should have obtained. (If you have trouble finding anything, try locating C and D on opposite sides of line .)

(c) Invent a Sketchpad construction that will produce triangles having the exact measurements given.

*See Theorem 2, Section 3.6.