Using Sketchpad, construct an equilateral ΔABC, and locate P any interior point. Measure t...

Using Sketchpad, construct an equilateral ΔABC, and locate P any interior point. Measure the distances PD, PE, and PF using Distance from the MEASURE menu. Call these distances x. y, and z, as shown in the figure. Calculate, and display, x + y + z.

(a) Drag P inside ΔABC and find what location(s) make the sum x + y + z a maximum and minimum. What behavior do you notice. Can you prove it?

b) Examine the sum.x + y + z when P lies outside ΔABC.