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Geometry · interactive lab

Triangle discovery sandbox

Drag three vertices to discover triangle types, area, perimeter, and the centroid.

Triangle discovery sandboxLIVE EXPLORATION
Drag a labeled point · enter coordinates for precision

Your measurements

Drag a vertex or enter coordinates. Use the challenges to discover how shapes behave.

Discovery challenges

Choose a goal, then move the vertices to find a solution. Classification uses a small numerical tolerance.

Why it works

Area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
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    A little question. A clearer picture.

    Triangle discovery sandbox: common questions

    Wondering about the why? Start here.

    What is the centroid of a triangle?

    The centroid is where the three medians meet. Each median joins a vertex to the midpoint of the opposite side. Average the three x-coordinates and the three y-coordinates to find the centroid; it divides each median in a 2:1 ratio from the vertex.

    Learn about triangle centers
    Why do points on a straight line not make a triangle?

    Three collinear points enclose no area, so they form a degenerate triangle. The sandbox asks you to move a point instead of treating that arrangement as a valid triangle. Overlapping vertices also cannot form a nondegenerate triangle.

    Explore triangle measurements