Question

Consider the terms pyramid, line, square, and triangle. The term____ is not defined in Euclidean geometry.

Answer 1

From the given terms line, pyramid, square, and triangle.

The term line is not defined in Euclidean geometry.

There are three words in geometry that are not properly defined.

These words are point, plane and line and are referred to as the "three undefined terms of geometry".

Answer 2

The term line is not defined in Euclidean geometry

Euclidean geometry

• Euclidean geometry is the study of planar and solid objects using the axioms and theorems of Euclid, a Greek mathematician.
• The study of geometrical shapes (plane and solid) and figures based on several axioms and theorems is known as Euclidean geometry. It is primarily intended for use on flat or plane surfaces. Geometry is derived from the Greek terms 'geo' (meaning earth) and 'metrein' (meaning 'to measure').
• The shapes of geometrical objects and planes are better explained using Euclidean geometry.
• The Greek mathematician Euclid used this aspect of geometry, which he also explained in his book Elements. As a result, this geometry is sometimes referred to as Euclid geometry.

Euclidean Geometry's Characteristics

• It entails the study of both plane and solid geometry.
• It established a point, a line, and a plane.
• A solid possesses shape, size, and position, as well as the ability to move from one location to another.
• A triangle's internal angles sum up to 180 degrees.
• Two parallel lines never intersect. A straight line is always the shortest distance between two places.

Euclid’s Five Postulates

1. From any point to another, a straight line can be traced.
2. A line that has been terminated can be produced endlessly.
3. Any centre and radius can be used to draw a circle.
4. Every right angle is the same as the one before it.
5. If a straight line intersecting two other straight lines produces interior angles on the same side of it that are less than two right angles when added together, the two straight lines will meet on the side where the sum of angles is less than two right angles if created endlessly.

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