MathPlotAI Logo MathPlotAI

Interactive Theorem & Proof Prompt: Perpendicular Bisector Theorem

Interactive Theorem & Proof Prompt: Perpendicular Bisector Theorem
Loading the math board and drawing, please wait…
2016-06-03 07:03
CircleCoordinate GeometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2
This example demonstrates the Perpendicular Bisector Theorem interactively, showing that if a point lies on the perpendicular bisector of a segment, it is equidistant from the endpoints. Key math concepts include perpendicular bisectors, distance equality, and geometric proofs. Constructed using GeoGebra commands like Segment, Midpoint, LineBisector, Circle, Intersect, CircleSector, Dilate, Rotate, Point, and Angle. Suitable for middle school and above students learning geometric theorems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(f) → C_1
  3. LineBisector(f) → p
  4. Circle(C_1, (0.1 * f)) → c
  5. Intersect(c, f, 2) → D
  6. Intersect(c, p, 2) → E
  7. CircleSector(C_1, D, E) → d
  8. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C_1) → A'
  9. Segment(A, A') → h
  10. Dilate(C_1, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  11. Segment(C_1, C') → i
  12. Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * π), (-π)], C_1) → A'_1
  13. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], C_1) → A''
  14. Segment(A'_1, A'') → h'
  15. Rotate(d, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], C_1) → d'
  16. Point(p) → C
  17. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], C) → A'_2
  18. Segment(A, A'_2) → g
  19. Dilate(B, If[1 < b ≤ 2, 2 - b, 0], C) → B'
  20. Segment(B, B') → j
  21. Angle(A, C, B) → α
  22. Rotate(A, If[2 < b ≤ 3, ((b - 2) * α), α], C) → A'_3
  23. Rotate(A'_2, If[2 < b ≤ 3, ((b - 2) * α), α], C) → G
  24. Segment(A'_3, G) → g'

AI Drawing Prompt Reference

Draw a segment with its midpoint and perpendicular bisector. Construct a small circle centered at the midpoint with radius one-tenth of the segment length, intersecting the segment and bisector to form a sector. Then animate: first, move a point along the segment and connect it to an endpoint; second, place a point on the bisector and connect it to both endpoints, showing the angle; finally, rotate the sector and related segments to illustrate that any point on the perpendicular bisector is equidistant from the segment's endpoints.
The prompt above was compiled from the original drawing commands and is for reference only.