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Geometry Space Lab
A 3D geometry lab: manipulate figures, construct auxiliary geometry and explain spatial angles and distances.
Choose a topic and an example. Orbit the figure to identify the objects being studied.
Reveal auxiliary geometry step by step, drag ringed points and observe. Every drag has an equivalent numeric control.
Use perpendicularity, parallelism and right triangles to explain. Readings support observation, but do not replace a proof.
Drag empty space to rotate; use the camera controls to zoom and frame. Blue handles adjust the same values as the parameter sliders.
θ / Step 1 · 4
≈ 36.9°
Where is the angle between SB and the base?
Target angle
θ · Rounded value
A is the perpendicular projection of S; B already lies in the base plane. Thus AB is the projection of SB and the required angle is ∠SBA. Changing the view does not change the angle.
In pyramid S.ABCD, SA is perpendicular to the base. Consider SB and plane (ABCD).
Drag S upwards while keeping AB = 4. Does the angle increase? Try SA = 3 for a 3–4–5 triangle.
Common misconception
The angle between SB and SA uses the normal to the base, not the projection of SB.