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Segment Addition Theorem Demo by Elaine Liu

Segment Addition Theorem Demo by Elaine Liu
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2015-10-04 07:35
VectorCoordinate GeometryGeometric Construction
This example demonstrates the Segment Addition Theorem, showing that the length of segment AC equals the sum of lengths of segments AB and BC by constructing them. Core math concepts include segment length, distance calculation, and geometric construction. Construction highlights: using Point to create points A, B, C, D; using Segment to draw segments AB, BC, CD; using Distance to measure segment lengths; using Text to label lengths; using Text1 to display the relationship. Suitable for middle school and above students learning geometric proofs and distance calculations, or for exploratory geometry teaching.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 5]) → B
  2. Segment(A, B) → a
  3. Point(Circle[B, 3]) → C
  4. Segment(B, C) → b
  5. Point(Circle[C, 5]) → D
  6. Segment(C, D) → c
  7. Distance(a, b) → d
  8. Distance(A, B) → distanceAB
  9. Distance(C, B) → distanceCB
  10. Distance(D, C) → distanceDC

AI Drawing Prompt Reference

Start with a point, then place a second point 5 units away, a third point 3 units further in the same direction, and a fourth point 5 units beyond that; connect consecutive points to form three segments, label each segment’s length, and show that the sum of the first two lengths equals the distance from the first to the third point, while the sum of all three equals the total distance from the first to the fourth point.
The prompt above was compiled from the original drawing commands and is for reference only.