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Constructing Congruent Triangles (SSS) in GeoGebra

Constructing Congruent Triangles (SSS) in GeoGebra
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2020-10-19 07:26
TriangleCirclePolygonAngleGeometric Construction
①This GeoGebra example demonstrates how to construct two congruent triangles using three given side lengths, visually confirming that corresponding sides and angles are equal. ②The core mathematical concept is the SSS (side-side-side) congruence criterion, along with the definition of congruent figures—identical in shape and size, superposable by rigid motions. ③Construction details: from the summary, the Polygon command creates the initial triangle poly1; Circle commands draw circles with radii equal to the given sides; Intersect finds the intersection points of circles to locate the third vertex; Segment connects vertices to form the new triangle. Objects include points A, B, C, A', C', segments a, b, d, e, f, g, h, i, j, and circles c, etc., reflecting a classic compass-and-straightedge approach. ④This is suitable for middle school geometry classes, helping students grasp congruence criteria, and can serve as an interactive tool to drag vertices and test whether congruence persists, or to compare SSS with SAS and other criteria.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(B, b) → d
  3. Circle(C, c) → e
  4. Intersect(d, e, 1) → A'
  5. Segment(B, A') → f
  6. Segment(C, A') → g
  7. Circle(A, a) → h
  8. Intersect(d, h, 2) → C'
  9. Segment(A, C') → i
  10. Segment(C', B) → j

AI Drawing Prompt Reference

Draw two congruent triangles with given side lengths AB=5, BC=6, and CA=7. First, draw triangle ABC. Then, draw a circle centered at B with radius AB, and another circle centered at C with radius BC. The intersection point A' of these two circles is the third vertex of the new triangle. Draw segments BA' and CA'. Next, draw a circle centered at A with radius AC, and find the intersection point C' of this circle with the previous two circles. Finally, draw segments AC' and C'B to form the congruent triangle A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.