Euclidean Geometry
Euclidean geometry is a mathematical system named after the ancient Greek mathematician Euclid
Euclidean geometry is a mathematical system named after the ancient Greek mathematician Euclid. It is one of the oldest branches of mathematics and deals with geometric shapes and their properties in a two-dimensional (2D) or three-dimensional (3D) space.
In Euclidean geometry, a point is a location in space with no size or dimension, a line is a straight path that extends infinitely in both directions, and a plane is a flat surface that extends infinitely in all directions.
Some important concepts in Euclidean geometry include:
1. Distance: The distance between two points in Euclidean space is the length of the straight line segment that connects them. This is typically calculated using the Pythagorean theorem.
2. Angle: An angle is formed by two rays with a common endpoint called the vertex. It is measured in degrees or radians and represents the amount of rotation needed to align one ray with the other. Right angles have a measure of 90 degrees.
3. Triangle: A triangle is a polygon with three sides and three angles. The sum of the angles in any triangle is always 180 degrees.
4. Congruence: Two geometric figures are congruent if they have the same shape and size. Congruent figures can be superimposed on each other by rigid motions such as translations, rotations, and reflections.
5. Similarity: Two geometric figures are similar if they have the same shape but not necessarily the same size. Similar figures can be obtained by uniformly scaling, flipping, or rotating one figure to match the other.
6. Parallel lines: Lines in the same plane that never intersect are called parallel lines. They have the same slope and will never converge or diverge.
Euclidean geometry provides the foundation for various mathematical theorems and proofs, allowing us to investigate the relationships between geometric objects and develop a deeper understanding of our physical world.
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