Plane Geometry
Plane Geometry is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install.
Drag the points and watch the theorems hold
Experiments
Angles in a triangle
The interior angles of every triangle add up to 180°. A line through C parallel to AB shows why: the angles α and β reappear at C as alternate angles.
Try this: Drag the vertices — the three angles change, their sum stays 180°.
Centres of a triangle
The altitudes meet at the orthocentre H, the medians at the centroid T, the perpendicular bisectors at the circumcentre O (centre of the circumscribed circle) and the angle bisectors at the incentre I (centre of the inscribed circle). H, T and O always lie on one line — the Euler line.
Try this: Switch the lines on one by one and drag a vertex — watch where each centre goes, e.g. outside an obtuse triangle.
Pythagorean theorem
In a right triangle, the square on the hypotenuse equals the sum of the squares on the two legs: a² + b² = c².
Try this: Drag A and B to change the legs — the areas of the squares always add up.
Thales’s theorem
Every angle inscribed in a semicircle is a right angle: if AB is a diameter and C lies on the circle, the angle ACB is 90°.
Try this: Move C along the circle, or move A and B — the angle at C stays 90°.
Central and inscribed angle
An inscribed angle is half of the central angle that stands on the same arc.
Try this: Move A, B and C along the circle and compare the two angles.
Similar triangles
Scaling a triangle by a factor k multiplies every side by k and the area by k²; the angles stay the same.
Try this: Drag the triangle or change k — compare the sides, the angles and the areas.
Frequently asked questions
What is Plane Geometry?
Plane Geometry is a free interactive simulation from StudyFi Lab. It runs right in your browser, with no sign-up and nothing to install. Drag the points and watch the theorems hold
Is Plane Geometry free?
Yes. Plane Geometry is completely free. It works in the browser on computers, tablets and phones, and you do not need an account.
What can I explore in Plane Geometry?
Angles in a triangle, Centres of a triangle, Pythagorean theorem, Thales’s theorem, Central and inscribed angle, Similar triangles.
What does the “Angles in a triangle” experiment show?
The interior angles of every triangle add up to 180°. A line through C parallel to AB shows why: the angles α and β reappear at C as alternate angles.
What does the “Centres of a triangle” experiment show?
The altitudes meet at the orthocentre H, the medians at the centroid T, the perpendicular bisectors at the circumcentre O (centre of the circumscribed circle) and the angle bisectors at the incentre I (centre of the inscribed circle). H, T and O always lie on one line — the Euler line.
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