Lab 4B
Midpoint relations
- Carry out the Quadrilateal Investigations at the very end of GASP
1 (from Lab 1). But ignore the questions about area.
Draw a triangle ABC and construct midpoints D, E, F as in the figure. Let
G be the intersection of the two medians CF and BD. Then let H be the midpoint
of BG and I be the midpoint of CG.
- Prove that DFHI is a parallelogram.
- Then use what you know about parallelograms to find the ratio BG/BD and
also CG/CF.
- Finally, repeat this construction for medians BD and AE, intersecting in
J. Can you prove G = J?
