- To draw a straight line from any point to any point.
- To create a finite straight line continuous in a straight line.
- To draw a Circle with any center and distance to describe.
- That all right angles are equal to each other.

Contents

- What are the 5 postulates of Euclid geometry?
- What are the basic postulates of geometry?
- How many postulates are given by Euclid?
- What is the first postulate of Euclidean geometry?
- What are the 5 theorems?
- What is Euclid fourth postulate?
- What is the another name of Euclid’s fifth postulate?
- What are the types of postulates?
- How many types of postulates are there?
- What is the 5th postulate connection to the study of non Euclidean geometry?
- Is Euclid’s 5th postulate inconsistent with the other four?
- What are postulate 3 of Euclid’s postulates?
- What are the 7 axioms of Euclid?
- How do you prove Euclid’s fifth postulate?
- What are the five 5 postulates for triangle congruence?
- How many theorems are there in Euclidean geometry?
- What is SSS SAS ASA AAS?
- Why is the 5th postulate of Euclid special?

Euclid’s postulates were: Postulate 1: A straight line can be drawn from any point to any other point. Postulate 2: A terminated line can be produced indefinitely. Postulate 3: A circle can be drawn with any center and any radius. Postulate 4 : All right angles are equal.

Postulate 1: There is exactly one straight line through any two points. Postulate 2: The measure of each line segment is a unique positive number. The measure (or length) of AB is a positive number AB. Postulate 7: If two points lie in a plane, then the connecting line lies in this plane.

There are **23** definitions or postulates in Book 1 of the Elements (Euclidean Geometry).

1. **A straight line segment can be drawn by connecting any two points**.

In particular, he is credited with proving the following five theorems: (1) a circle is bisected by any diameter; (2) the base angles of an isosceles triangle are equal; (3) the opposite (“vertical”) angles formed by the intersection of two lines are equal; (4) two triangles are congruent (of the same shape and size…

This postulate states that **an angle at the base of a perpendicular, such as B. angle ACD, is equal to an angle at the base of every other perpendicular, such as. B. Angle EGH**. This postulate forms the basis of angle measurement. The only angle measurement that occurs in the elements refers to right angles.

The converse of the **parallel postulate**: if the sum of the two interior angles equals 180°, then the lines are parallel and will never intersect.

- Postulat
- Postulat
- Postulat
- Postulat 5 oder Linealpostulat.
- Postulat 6 oder Segmentadditionspostulat.
- Postulat 7 oder Winkelgradpostulat.
- Postulat 8 oder Winkeladditionspostulat.
- Postulat

A postulate is a statement that is assumed to be true without proof. A theorem is a true statement that can be proved. Below are **six postulates** and the theorems that can be proved from those postulates. Postulate 1: A straight line contains at least two points.

Euclid’s fifth postulate, **the parallel postulate**, corresponds to Playfair’s postulate, which states that within a two-dimensional plane, for any given line l and one point A that does not lie on l , there exist exactly a straight line through A that does not intersect l.

**It is clear that the fifth postulate differs from the other four**. It didn’t satisfy Euclid and he tried to avoid using it for as long as possible – in fact the first 28 theorems of the elements are proved without using it.

3. **Any straight line segment can be drawn into a circle that has the segment for radius and an endpoint for center**.

The 7 axioms are: **Things that are equal are equal to each other.** **When like is added to like, the wholes are equal.** **When like is of equal is subtracted, the remainders are equal**.

If a line falling on two lines makes the sum of the interior angles on the same side less than two right angles, then the two lines, when they arise indefinitely, meet on the side on which the sum of the angles is less than two right angles angle is.

Summarizing the above material, the **five** most important theorems of planar Euclidean geometry are: the sum of the angles in a triangle is 180 degrees, the bridge of donkeys, the fundamental theorem of similarity, the Pythagorean theorem and the invariance of angles subtended by a chord in a circle.

Congruence conditions for triangles:

**SSS (Side-Side-Side)** **SAS (Side-Angle-Side)** **ASA ( Angle-Side-Angle)** **AAS (Angle-Angle-Side)** **RHS (Right Angle-Hypotenuse-Side)**

Along with 23 definitions and several implicit assumptions, **Euclid derived much of planar geometry from five postulates**. A straight line can be drawn between any two points. A piece of straight line can be extended as desired.

- https://ncert.nic.in/textbook/pdf/iemh105.pdf
- https://www.cerritos.edu/dford/SitePages/Math_70_F13/PostulatesandTheorems.pdf
- https://www.toppr.com/guides/maths/introduction-to-euclids-geometry/euclids-postulates/
- https://mathworld.wolfram.com/EuclidsPostulates.html
- https://www.britannica.com/topic/Thales-rectangle-1688495
- http://aleph0.clarku.edu/~djoyce/java/elements/bookI/post4.html
- https://en.wikipedia.org/wiki/Parallel_postulate
- https://www.basic-mathematics.com/geometry-postulates.html
- https://www.cliffsnotes.com/study-guides/geometry/fundamental-ideas/postulates-and-theorems
- https://en.wikipedia.org/wiki/Non-Euclidean_geometry
- https://mathshistory.st-andrews.ac.uk/HistTopics/Non-Euclidean_geometry/
- https://people.math.harvard.edu/~ctm/home/text/class/harvard/113/97/html/euclid.html
- https://www.cuemath.com/geometry/euclids-geometry/
- https://byjus.com/maths/euclid-geometry/
- https://chitowntutoring.com/congruence-theorem-triangles/
- https://www.britannica.com/science/Euclidean-geometry/Plane-geometry
- https://byjus.com/maths/congruence-of-triangles/
- https://www.cut-the-knot.org/triangle/pythpar/Fifth.shtml

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