Plot three points to create triangle ABC using the point tool.
Use the midpoint tool (under the point tool) to find the midpoint between points A and C. Use the same process to find the midpoint between points B and C.
Connect the following pairs of points with a segment using the segment tool (under the line tool): A and D, C and D, C and E, E and B, A and B, D and E.
Right click on each segment, and under Object Properties select Show Label. In the dropdown box, select Value.
Answer the following questions:
1) What is the relationship between triangles ABC and DEC (congruent, similar, none)?
2) Justify your answer to #1 (how do you know, prove it).
3) What is the ratio from ABC to DEC?
4) What is the ratio from AB to DE?
Use the angle tool to find the measures of angles CED and EBA.
5) What is the relationship of these two angles?
6) What does that tell us about DE and AB?
Press the refresh button and go through this process again, but change some of the values (make a different kind of triangle, use different sides of your triangle to create a midsegment) and answer questions 1 through 6 again.
7) Based on your answers to the questions above, what are some things that will always be true of a midsegment of a triangle? Be as specific as possible.