2 [Deleted User] Asked: November 7, 20202020-11-07T18:25:29+05:30 2020-11-07T18:25:29+05:30In: Maths What are Euclid’s postulates? 2 What are Euclid’s postulates? question Share Facebook 4 Answers Voted Oldest Recent [Deleted User] 2020-11-08T16:49:40+05:30Added an answer on November 8, 2020 at 4:49 pm Postulate – I A straight line segment can be formed by joining any two points in space. In 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. Postulate – 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. 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. 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. 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. ‘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 Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Mehul Jhumri telaiya , India 326 Questions 988 Answers 8 Best Answers 127 Points View Profile Mehul Rookie 2020-11-07T19:00:54+05:30Added an answer on November 7, 2020 at 7:00 pm 1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight lines segment, a circle can be drawn having the segment as radius and one endpoint as center. 4. All Right Angles are congruent. 5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two Right Angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the Parallel Postulate. 3 Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Ritik kumar 248 Questions 725 Answers 3 Best Answers 99 Points View Profile Ritik kumar Rookie 2020-11-14T10:36:54+05:30Added an answer on November 14, 2020 at 10:36 am The five postulates on which Euclid based his geometry are: To draw a straight line from any point to any point. To produce a finite straight line continuously in a straight line. To describe a circle with any center and distance. That all right angles are equal to one another. 0 Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Shivansh Preet Chandwara, koderma, India 63 Questions 585 Answers 31 Best Answers 228 Points View Profile Shivansh Preet Competent 2020-11-08T05:43:47+05:30Added an answer on November 8, 2020 at 5:43 am 1. To draw a straight line from any point to any point. 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any center and distance. 4. That all right angles are equal to one another. 5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, The two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. 0 Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp You must login to add an answer. Username or email* Password* Remember Me! Forgot Password?