About this explorer
Euclid organized geometry as a chain of definitions, common notions, postulates, and propositions in The Elements. This explorer focuses on selected results from Book I and Book III.
Use each diagram as an experiment: move a point, predict what will happen, and compare your prediction with the live measurements. The proof sketch then connects the visual pattern to the mathematical reasoning.
Modern theorem names are used alongside the proposition numbers. A few demonstrations combine a classical construction with a familiar modern consequence, and these are labeled clearly.
Geometry glossary
Useful words for the demonstrations in this explorer.
- Acute angle
- An angle smaller than 90 degrees.
- Chord
- A line segment joining two points on a circle.
- Diameter
- A chord that passes through the center of a circle.
- Exterior angle
- An angle outside a polygon formed by extending one side.
- Isosceles triangle
- A triangle with two equal sides and two equal base angles.
- Obtuse angle
- An angle greater than 90 degrees and smaller than 180 degrees.
- Parallel lines
- Lines in the same plane that never meet.
- Parallelogram
- A quadrilateral with both pairs of opposite sides parallel.
- Radius
- A segment from a circle's center to its circumference.
- Segment of a circle
- A region bounded by a chord and its corresponding arc.
- Tangent
- A line that touches a circle at one point.
- Vertical angles
- Opposite angles formed when two lines intersect.
