Certain inequality problems lend themselves to the Sketchpad software, as the following p...

Certain inequality problems lend themselves to the Sketchpad software, as the following project will show.

[1] Construct segment then rays and

[2] By rotating ray about A and about B, construct angles at A and B having measures 43 and 36, respectively (for rotation about B, use -36°).

[3] Select the point of intersection C of the two rotated rays, then hide all four rays. Finally, construct segments and . You should now have a triangle ∆ABC with m∠A = 43 and m∠B = 36.

[4] Construct a point D on segment , and join points C and D.

[5] Display the angle measures x = m∠ADC and y = m∠DCB.

Now drag point D, beginning at A and ending at B. As you do so, watch die values of x and y change.

(a) What are the smallest and largest values that x seems to attain. Write down the resulting inequality.

(b) Repeat for the value of y.

(c) Use the inequalities established in this section to prove the inequalities you obtained in (a) and (b).