Geometry Theorem 5.7.4 Illustration - Parallelism and Triangle Area

Consider the parallel lines m and n. BC is a fixed segment on line m, and A is a variable point on line n. Move A along line n. Note what happens to the side lengths and the area of the triangle.

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1. What happens to the side lengths? To the area?
2. Why do you think the area of the triangle remains the same even though the side lengths change?
3. Using the buttons provided, do the following:

  • a. Construct perpendicular lines between lines m and n.
  • b. Plot the intersection points of this line with lines m and n.
  • c. Draw a segment between those two points.
  • d. Find the length of this segment.
4. Convince yourself why the area of the triangle remains the same in this situation. Write up an explanation as to why this is true.

Mindy Burcham, Created with GeoGebra