Triangle Proportionality Theorem Discovery
Step 1: Use the "parallel line" tool to construct a line parallel to Segment AC through point D.
Step 2: Create point E where the parallel line intersects side BC.
Question 1: Is Triangle BDE similar to Triangle BAC? How do you know? (Measure angles EDB, BED, CAD, and ECA).
Step 3: Use the "Distance or Length" tool to measure BD, DA, BE, and EC.
Step 4: Set up the following ratios:
Question 2: What do you notice about those ratios? Make a different triangle, and write the two ratios again? Does the relationship still hold?
Question 3: All of this was based on line DE being parallel to side AC. If you constructed a line not parallel to AC through point D, would the triangles still be similar? Explain why or why not.