Geometry

Draw points, lines, segments, circles and polygons on an interactive board, then drag any point and watch lengths, angles and areas update live. It works like a friendly mini-GeoGebra — free, no sign-up, and everything runs in your browser.

How to use the Geometry tool

1. Pick a tool from the toolbar — Point, Segment, Circle, Polygon and more. The hint bar under the canvas always tells you what to click next.
2. Click on the canvas to place points and build your figure. Clicking near an existing point reuses it, so shapes join up neatly.
3. Switch to the Move tool and drag any point — every length, angle and area in the Objects list updates instantly.
4. Use Undo if you make a mistake, zoom and Fit to frame your work, and Export PNG to save the finished drawing.

What is geometry?

Geometry is the branch of mathematics that studies shapes, sizes and positions. It starts from simple building blocks — points, lines and angles — and builds up to triangles, circles and solids. Because it is so visual, the fastest way to learn geometry is to draw a figure and experiment with it, which is exactly what the board above is for: drag the corners of the starter triangle and see which measurements change and which stay the same.

Points, lines, segments and rays

A point is an exact position with no size, named with a capital letter such as A. A line is straight, has no thickness, and continues forever in both directions. A line segment is the part of a line between two endpoints, so it has a fixed length you can measure — segment AB above is a segment. A ray starts at one endpoint and continues forever in one direction, like a torch beam. Two lines in a plane are parallel if they never meet, and perpendicular if they meet at a right angle (90°). The toolbar has tools for all of these: draw a segment, extend it to a full line, or construct parallels and perpendiculars through any point.

Circles: centre, radius and diameter

A circle is the set of all points at the same distance from a centre point. That distance is the radius (r). The diameter (d) passes through the centre and is twice the radius: d = 2r. The distance around the circle is the circumference, C = 2πr, and the space inside is the area, A = πr². With the Circle tool, the second point you click sets the radius — drag it and the Objects list shows the radius, circumference and area changing together. A line from an outside point that touches the circle at exactly one point is a tangent; try the Tangent tool and drag the point to see both tangents follow it.

Angles and their types

An angle measures the turn between two lines that meet at a point called the vertex. Angles are measured in degrees (°), and a full turn is 360°. To measure one with the Angle tool, click a point on one side, then the vertex, then a point on the other side — the vertex always goes in the middle.

Two useful constructions split angles and segments exactly in half: an angle bisector is a line through the vertex that divides an angle into two equal parts, and a perpendicular bisector crosses a segment at its midpoint at 90°. Both tools are in the Construct section of the toolbar, and both update live when you drag the original points.

Area and perimeter formulas

The perimeter of a shape is the total distance around its edge, and its area is the surface it covers, measured in square units. These are the formulas the Area tool uses:

For any polygon, this tool adds up the edge lengths for the perimeter and uses the shoelace method for the area, so even irregular shapes you draw freehand get exact measurements.

Worked example: the 3-4-5 right triangle

The triangle loaded on the board has vertices A(0, 0), B(4, 0) and C(0, 3). The Objects list shows AB = 4.00, AC = 3.00 and BC = 5.00, and the angle at A is exactly 90°, so this is a right triangle. Pythagoras' theorem says that in a right triangle the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides: a² + b² = c². Check it with these lengths: 3² + 4² = 9 + 16 = 25, and 5² = 25. It works. The area is ½ × base × height = ½ × 4 × 3 = 6.00 square units, matching the polygon's area in the list. Now drag point B to the right: the hypotenuse and area grow, the angle at A stays 90° because AC is still vertical and AB still horizontal — and Pythagoras keeps holding for every new set of lengths.

Common mistakes

• Mixing up radius and diameter. The diameter is the full width through the centre, twice the radius. Using d where a formula needs r doubles or halves your answer.
• Putting the vertex at the end. When measuring an angle, the vertex (corner) point is the middle click. Any other order measures a different angle.
• Forgetting square units for area. Lengths are in units, but areas are in square units (units²) because they count covered squares.
• Assuming a drawing is exact. A figure that looks like a right angle may only be 89.6°. Trust the measured value in the Objects list, not your eye.

Frequently asked questions

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