Basic Geometric Construction Simulator

Math Geometry • Basic Shapes and Properties

Written by STEM Calculators Team Published January 21, 2026 Updated February 24, 2026

Geometric Construction Calculator – Bisectors, Perpendiculars & More

Interactive compass & straightedge constructions. Drag the base points to see the construction update. Use Prev/Next (or Play) to reveal steps.

Construction

Choose a construction:

Display

Show compass arcs/circles (guides)

Show point labels

Snap to nice view on mode change

Speed & precision

Play speed

Pan: drag empty space • Zoom: wheel/trackpad • Drag points to move them.

Quick examples

“Fill example” loads a clean setup for the chosen construction.

Ready

Choose a construction, then click Next to reveal steps.

Construction canvas (pan/zoom + draggable points)

Tip: If circles overlap weirdly, drag points farther apart.

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Basic Geometric Construction Simulator – Bisectors, Perpendiculars & More

Step-by-step compass & straightedge constructions online: angle bisector, perpendicular, equilateral triangle & more. Interactive geometry tool.

Compass & Straightedge Constructions

Classical Euclidean constructions allow only:

Circles/arcs (a compass): choose a center and radius.
Straight lines (a straightedge): draw a line through two known points.

Many geometric tasks reduce to finding intersection points of circles and lines. This simulator animates that process step-by-step, and lets you drag the starting points to see the construction update.

1) Perpendicular Bisector of Segment \(AB\)

Given segment \(\overline{AB}\).
Set compass width to \(AB\). Draw circles centered at \(A\) and \(B\) with radius \(AB\).
Mark the intersection points \(X\) and \(Y\).
Draw line \(XY\). This is the perpendicular bisector of \(\overline{AB}\).

Why it works: points \(X\) and \(Y\) are equidistant from \(A\) and \(B\), so \(XY\) is the locus of points with \(XA=XB\), which is the perpendicular bisector.

2) Angle Bisector of \(\angle ABC\)

Start with rays \(BA\) and \(BC\) forming \(\angle ABC\) at vertex \(B\).
Draw an arc centered at \(B\) intersecting the rays at \(E\) and \(F\).
With equal compass width, draw arcs centered at \(E\) and \(F\). Let them intersect at \(G\).
Draw ray \(BG\). This bisects \(\angle ABC\).

Key idea: triangles \( \triangle BEG \) and \( \triangle BFG \) share side \(BG\) and have equal construction radii, forcing equal angles at \(B\).

3) Perpendicular Through a Point \(P\) to Line \(AB\)

Draw a circle centered at \(P\) that cuts line \(AB\) at two points \(E\) and \(F\).
Draw equal circles centered at \(E\) and \(F\). Let them intersect at \(X\) and \(Y\).
Draw line \(XY\). This line is perpendicular to \(AB\) and passes through \(P\).

4) Equilateral Triangle on Segment \(AB\)

Set compass width to \(AB\). Draw circles centered at \(A\) and \(B\) with radius \(AB\).
Choose one intersection as vertex \(C\).
Draw segments \(\overline{AC}\) and \(\overline{BC}\). Then \(AB=BC=CA\), so \(\triangle ABC\) is equilateral.

Tips for Using the Simulator

Drag points to change the starting geometry.
Use Prev/Next to reveal steps, or Play to animate automatically.
Turn on guides to see compass circles/arcs.
If intersections disappear, move points farther apart (the construction may not be well-defined in that configuration).

Frequently Asked Questions

What is a compass and straightedge construction?

It is a classical Euclidean method that allows only two actions: drawing circles/arcs with a compass and drawing straight lines through known points with a straightedge. Many constructions work by creating intersection points of circles and lines.

How does the perpendicular bisector construction work?

Draw equal-radius circles centered at A and B so they intersect at two points X and Y. The line XY is the set of points equidistant from A and B, so it is perpendicular to AB and passes through the midpoint of AB.

How do you construct an angle bisector for angle ABC?

Draw an arc centered at B that cuts rays BA and BC at two points, then draw equal-radius arcs from those two points to meet at a new point. The ray from B through that intersection point divides angle ABC into two equal angles.

Why do the compass circles sometimes not intersect in the simulator?

If the chosen radius and the point positions make the circles too far apart or one circle fully contains the other, there may be zero intersection points. Spreading the base points farther apart can restore a well-defined intersection.

What do Prev, Next, and Play do in the construction simulator?

They control how the construction is revealed. Next shows the next construction step, Prev goes back a step, and Play animates the steps automatically at the selected play speed.

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Frequently Asked Questions

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