SMSG Model Interactive Learning
Euclidean geometry is a mathematical system attributed to the ancient Greek mathematician Euclid. His work "Elements" is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics from its publication until the late 19th or early 20th century.
The SMSG (School Mathematics Study Group) model organizes Euclid's postulates in a way that makes them more accessible to modern students. Explore each postulate through interactive simulations below.
Through any two distinct points, there is exactly one line.
Click on the canvas to place two points. A line will be drawn through them.
This postulate states that given any two distinct points, there exists exactly one line that passes through both points. This is a fundamental concept in Euclidean geometry and forms the basis for many geometric constructions.
A line segment can be extended indefinitely into a line.
Click "Extend Line" to see how a line segment can be extended.
This postulate states that any line segment can be extended infinitely in both directions. This implies that lines in Euclidean geometry have no end points and extend indefinitely.
Given a point and a distance, a circle can be drawn with the point as center and the distance as radius.
Click on the canvas to place a center point. Adjust the slider to change the radius.
This postulate states that given any point and a distance, you can construct a circle with that point as the center and the distance as the radius. This is a fundamental construction in geometry that allows us to create circles of any size at any location.
All right angles are congruent (equal in measure).
Click "Show Right Angles" to display different right angles. Click "Rotate" to see that they remain congruent even when rotated.
This postulate states that all right angles are equal in measure (90 degrees). This might seem obvious to modern students, but it is a critical assumption in Euclidean geometry because it establishes a standard unit of angular measure.
Through a point not on a given line, there is exactly one line parallel to the given line.
Click "Show Parallel Line" to display a line parallel to the given line through the point. Click "Move Point" to change the point's position.
The Parallel Postulate states that given a line and a point not on that line, there exists exactly one line passing through the point that is parallel to the original line. This postulate is perhaps the most famous of Euclid's postulates and led to the development of non-Euclidean geometries in the 19th century.
1. Which postulate states that through any two distinct points, there is exactly one line?
2. Which postulate states that a line segment can be extended indefinitely into a line?
3. Which postulate allows us to create circles?
4. Which postulate states that all right angles are congruent (equal in measure)?
5. The Parallel Postulate is also known as: