Interactive Geometry Lab
Drag the points and watch every measurement update live. Switch between triangle and circle modes.
The formulas behind the numbers
- Triangle area: half the absolute value of the cross product of two sides, which equals base times height over 2.
- Triangle angles: from the law of cosines applied to the three side lengths; they always sum to 180 degrees.
- Circle: radius is the distance from center to edge; circumference is 2 times pi times radius; area is pi times radius squared.
- Distances use the Pythagorean theorem on the point coordinates.
Why use an interactive figure
Formulas stick better when you can feel them. Drag a triangle vertex and watch the area stay constant when you slide it parallel to the base. Drag the circle edge and see circumference grow in exact proportion to the radius. That is the relationship the formulas describe, made visible.
Frequently asked questions
What can I drag?
In triangle mode drag any of the three corner points. In circle mode drag the center or the edge point to resize.
Are the measurements exact?
They are computed live from the point positions with standard geometry formulas, shown to two decimals.
What is this good for?
Building intuition: watch how area, angles and circumference respond as you reshape the figure, then check the formulas behind the numbers.
Does it work on touch screens?
Yes. The points use pointer events, so dragging works with mouse, touch and pen.