Question

Part 1: On your own paper, create a triangle having different measures of the three vertex angles. You do not have to measure the actual angles. Provide a description of your triangle including which angle is the largest and which is the smallest.

Part 2: Using the triangle created in Part 1, write the correct order of the lengths of the sides from the greatest to the least.

Part 3: Justify your answer for Part 2.

Answer 1

Part I, you just draw a good old fashioned vanilla scalene triangle. I personally would go for a right-triangle and draw one of the legs including the right angle to be obviously longer than the other, like this:

of course, you can go with anything that looks good for you. :)

Part II; the goal here is to look at which angle is 'biggest'. This angle is opposite the largest side (this is essentially the angle "widening" the triangle for that opposite side, if you look at it). Similarly, the smallest angle is opposite the smallest side. That would leave the last angle, which is in the middle in terms of measure, as is its length.

Part III, I guess you'd just explain what I just said, since that's about the idea you're looking at (maybe you have a specific theorem for this that you can reference as well)