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Explore compass-and-ruler constructions with animated, clickable steps and accurate diagrams.
Free Online Geometry Tool | CBSE • ICSE • State BoardsClick Start Construction to begin.
🔵 Blue = final construction lines. 🟣 Purple dashed = compass arcs and auxiliary lines. One drawing unit represents 40 screen units; drawings are schematic but constructed using geometric relationships. Use a ruler and compass to reproduce them on paper.
Select a construction, enter the required measurements, and press Start Construction. Use Next Step to reveal each compass or ruler action. Press Previous to revise a step, Show All to view the complete construction, or Reset to begin again. The geometric measurements determine the displayed figure, while the board automatically scales drawings to fit.
Geometrical construction means drawing mathematical figures precisely by following a sequence of ruler-and-compass operations. A straightedge is used to draw straight lines, while a compass draws circles and arcs of equal radius. Classical constructions include perpendicular bisectors, angle bisectors, 60-degree and 90-degree angles, and triangles formed from specified side lengths or angles. These skills develop spatial reasoning and help students understand why geometric theorems work.
Draw line segment AB. Open the compass to a radius greater than half of AB. With A as centre, draw arcs above and below AB. Keeping the same compass opening, repeat from B so that the arcs intersect at P and Q. Draw line PQ. It meets AB at its midpoint M and makes a right angle with AB. Any point on PQ is equidistant from A and B.
Draw an angle with vertex O. From O, draw an arc intersecting both arms at P and Q. Using equal compass radii, draw intersecting arcs from P and Q inside the angle. Join O to their intersection R. The ray OR divides the original angle into two equal angles.
For SSS construction, draw the base AB, draw a circle or arc from A with radius AC, and another from B with radius BC. Their intersection gives C. Join AC and BC. The three lengths must satisfy the triangle inequality: the sum of any two sides must exceed the third. For SAS construction, draw AB, construct the included angle at A, mark AC along the new ray, and join C to B. These methods determine a triangle up to reflection.
Always label important points clearly. Keep the compass radius unchanged when a step requires equal arcs. Draw auxiliary arcs lightly, then darken the required figure. Check whether an angle is acute, right, or obtuse before starting. When drawing triangles, verify that the given measurements can form a valid triangle. Finally, describe each construction step in mathematical language rather than relying only on the picture.
Which tool is used to draw an arc?
Select an answer.
Score: 0 / 0
Yes. Choose Triangle (SSS), enter three valid side lengths, and follow the arc-intersection steps.
Yes. Dashed purple arcs illustrate the compass movements used in the constructions.
Draw equal-radius intersecting arcs from the two endpoints of a segment and join the arc intersections.
Yes. The interface adapts to smaller screens and the buttons can be tapped.
The underlying geometry uses calculated intersections and angles. Figures are automatically scaled to fit the drawing board.
A protractor can measure angles, but classical ruler-and-compass construction relies on copying distances and intersecting arcs.