1. Define postulates
2. state Euclids postulate
3. what are undefined objects in Euclids geometry
Answers
Answer:
1)A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven. Listed below are six postulates and the theorems that can be proven from these postulates. Postulate 1: A line contains at least two points.
2)Postulate – I
A straight line segment can be formed by joining any two points in space.
Euclid GeometryIn Geometry, a line segment is a part of a line that is bounded by 2 distinct points on either end. It consists of a series of points bounded by the two endpoints. Thus a line segment is measurable as the distance between the two endpoints. A line segment is named after the two endpoints with an overbar on them.
Euclid GeometryPostulate – II
Any straight line can be extended indefinitely on both sides. Unlike a line segment, a line is not bounded by any endpoint and so can be extended indefinitely in either direction. A line is uniquely defined as passing through two points which are used to name it.
Euclid Geometry
Postulate – III
A circle can be drawn with any centre and any radius. For any line segment, a circle can be drawn with its centre at one endpoint and the radius of the circle as the length of the line segment. Consider a line segment bounded by two points. If one of these points is taken as the centre of a circle and the radius of the circle is taken as equal to the length of the segment, a circle can be drawn with its diameter twice than the length of the line segment.
Euclid Geometry
In the above example, the line segment AO serves as the radius of a circle with centre at point O and a diameter equal to AB where l(AB) =2l(AO).
Postulate – IV
All right angles are congruent or equal to one another. A right angle is an angle measuring 90 degrees. So, irrespective of the length of a right angle or its orientation all right angles are identical in form and coincide exactly when placed one on top of the other. by
Euclid Geometry
A right angle
Postulate – V
Two lines are parallel to each other if they intersect the third line and the interior angle between them is 180 degrees.
Image result for parallel lines‘Parallel lines’ are a set of 2 or more lines that never cross or intersect each other at any point in space if they are extended indefinitely. As you can see in the above image, line 1 and line 2 are parallel if and only if the sum of angles ‘a’ and ‘b’ they make with the transversal is 180 degrees.
3)These words are point, line and plane, and are referred to as the "three undefined terms of geometry".
Answer:
A step by step that is believed or accepted to be true, that forms the basis of a theory etc.
Step-by-step explanation:
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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