Geometry began with Euclid, who built it from a few clear definitions, a handful of axioms and postulates accepted without proof, and theorems proved by logic. Learn how a point, a line and a surface are defined, what Euclid's five postulates say, and how we prove that two distinct points fix exactly one line. Tap each idea to explore.
Play with it
Geometry starts from a few simple words. Tap each one to see what Euclid meant — and how definitions, axioms and proved theorems fit together.
Learn
Worked example. How many lines can pass through two distinct points A and B?
Try it: attempt to draw a second straight line through both A and B — every attempt lands on the same line.
Why: Euclid’s postulate guarantees a line joining any two points, and that line is unique.
Answer: exactly one line passes through two distinct points.
Where you'll meet it
Euclid’s pattern — start from a few accepted truths and prove everything else by logic — is how all of mathematics works. Whether you prove a property of triangles or a result in algebra, you are using his axiom-to-theorem method of careful, step-by-step reasoning.
Architects, engineers and CAD software rely on Euclidean geometry — points, straight lines, circles and the rule that two points fix one line — to draw accurate plans, layouts and 3D models that fit together exactly.
Check yourself
Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.
Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 9 Mathematics textbook (ncert.nic.in).
Buffyyour study buddyBuffy is an AI helper and can be wrong — always check your NCERT textbook.