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Geometry That Survives Dragging

Move C through four positions and separate what stays equal from what only looks fixed.

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A and B stay at (-4, 0) and (4, 0). C moves on x = 0. Which claim survives all four trials within a 0.01-unit tolerance?

CA and CB stay equal in every trial.The angle at C stays the same in every trial.

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Use the difference |CA − CB| as your test. A changing angle cannot disprove an equal-distance invariant.

About this activity

What you practise: Test a new constrained construction at four positions, record one invariant and one changing measurement, and explain why one drawing is insufficient.

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A and B stay at (-4, 0) and (4, 0). C moves on x = 0. Which claim survives all four trials within a 0.01-unit tolerance? A sits at (−4, 0) and B at (4, 0). C is moved to four places on the line x = 0. For each place the model lists the lengths CA and CB and the angle at C. In all four trials CA equals CB, for example 5.00 and 5.00 or 10.77 and 10.77. C always lies on x = 0, the perpendicular bisector of AB, and every point there is equally far from A and B. The angle at C, by contrast, changes from 43.5° to 126.9°.