Perpendicular Bisector Definition

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2019-06-24 22:26

This example demonstrates the definition of a perpendicular bisector. Key mathematical concepts include line segments, circles, and perpendicular bisectors. By constructing line segments, midpoints, perpendicular bisectors, circles, and intersections, students can understand the properties of perpendicular bisectors. Suitable for middle school and above students for geometric construction.

GeoGebra Commands & Parameters

Segment(A, B) → f
Midpoint(f) → C
LineBisector(f) → p
Circle(C, (0.1 * f)) → c
Intersect(c, f, 2) → D
Intersect(c, p, 2) → E
CircleSector(C, D, E) → d
Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'
Segment(A, A') → h
Dilate(C, If[1 < a ≤ 2, 2 - a, 0], B) → C'
Segment(C, C') → i
Rotate(A, If[2 < a ≤ 3, ((-(a - 2)) * π), (-π)], C) → A'_1
Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], C) → A''
Segment(A'_1, A'') → h'
Rotate(d, If[3 < a ≤ 4, ((a - 3) * π / 2), π / 2], C) → d'

AI Drawing Prompt Reference

Draw a line segment AB, find its midpoint C, and then draw the perpendicular bisector p of AB. Draw a circle c with C as the center and the length of AB divided by 10 as the radius, and find the two intersection points D and E of circle c and line segment AB, then connect D and E. Next, draw line segment AA', then draw a circle c' with C as the center and the length of line segment AA' as the radius, and find the two intersection points C' and A'' of circle c' and line segment AA', then connect C' and A''. Finally, rotate line segment DE 90 degrees around point C to get line segment DE', rotate line segment AA' 180 degrees around point C to get line segment A'A'', and rotate line segment DE' 270 degrees around point C to get line segment DE''.

The prompt above was compiled from the original drawing commands and is for reference only.