Euclidean and non Euclidean geometries problems

• nmego12345
In summary, the conversation was about a student seeking to verify their solutions to problems in a math book. They asked for help with 10 questions and received advice that it is better to ask for help with one question at a time. The conversation ended with the idea that the student should seek help from friends at their university.
nmego12345
So I was reading this book, "Euclidean and non Euclidean geometries" by Greenberg
I solved the first problems of the first chapter, and I would like to verify my solutions

1. Homework Statement

Homework Equations

[/B]
Um, none that I can think of?

The Attempt at a Solution

(1) Correct
(2) It is defined as: "An "angle with vertex A" is a point A together with two distinct nonopposite rays AB and AC (called the sides of the angle) emanating from A
We're asked if it is defined as the space between two rays that emanate from a common point
I think that's incorrect
(3) Incorrect
(4) Incorrect (2 lines are parallel if they don't intersect)
(5) Incorrect (it wasn't proven)
(6) Correct
(7) Incorrect (it is a right angle if it has a supplementary angle to it to which it is congruent
(8) Correct
(9) Correct
(10) Correct

Definitions:
1. (a) Midpoint M of a segment AB
M is the midpoint of the segment AB if M lies on segment AB where the segment MA is congruent to the segment MB
1. (b) Perpendicular bisector of a segment AB
l is the Perpendicular bisector of the segment AB if the line l is perpendicular to line AB (we've already defined that two lines (l, m) are perpendicular if they intersect at a point A and if there is a ray AC that is part of l and a ray AC that is part of M such that angle BAC is right angle) and if the point of intersection of the lines l and AB is also the midpoint of the segment AB
1. (c) Ray BD bisects angle ABC if angle ABD is congruent to the angle CBD
1. (d) Points A, B, and C are collinear, if the rays BA and BC are opposite
1. (e) lines l, m and n are concurrent if the lines l and m intersect at a point A and the lines m and n intersect at point A as well

2.(a) The triangle ABC formed by three collinear points A, B and C is the set of points that lie on the segment AB + the set of points that lie on the segment BC + the set of points that lie on the segment CA
2.(b) The vertices of ABC are the three points that lie on the triangle ABC in which if we draw line segments joining the 3 of them, we'll get a triangle congruent to triangle ABC
The sides of ABC are the 3 segments that lies on the triangle ABC where the first and second segment intersect at the first vertex, the second and third segment intersect at the second vertex, and the third and first segment intersect at the third vertex
The angles of ABC are the 3 angles in which each angle is formed of the union of a vertex of tirangle and the 2 rays that emanate from that vertex in which the two sides that intersect at the vertex each of them is part of one of the 2 rays.
(Should I say that they are called angles ABC, CAB and ACB or I don't have to?)
I want to safecheck my solutions before solving other problems

Last edited:
Anyone, help?

I guess it is hopeless

No one is going to read a post this long just to confirm it for you. You've asked 10 questions in one post!
This is something you can do with your friends at university.

nmego12345 said:
I guess it is hopeless

carpenoctem said:
No one is going to read a post this long just to confirm it for you. You've asked 10 questions in one post!
This is something you can do with your friends at university.

Indeed. Asking for people to check your answers is unlikely to get many responses. You're far more likely to get a response if you post a single question that you're having trouble with and want to talk about. PF isn't really a homework-checking site. There are plenty of those elsewhere.

1. What is the difference between Euclidean and non-Euclidean geometries?

Euclidean geometry is the traditional geometry that we learn in school, where the fundamental rules include the parallel postulate and the Pythagorean theorem. Non-Euclidean geometries, on the other hand, do not adhere to these rules and may have different concepts of parallel lines and distance measurements.

2. How do non-Euclidean geometries challenge our understanding of space and geometry?

Non-Euclidean geometries challenge our understanding of space and geometry by introducing different concepts and rules that may contradict our traditional understanding. For example, in hyperbolic geometry, the sum of the angles of a triangle can be less than 180 degrees, which goes against the parallel postulate in Euclidean geometry.

3. What are some real-world applications of non-Euclidean geometries?

Non-Euclidean geometries have many real-world applications, such as in the study of curved spaces in general relativity, the navigation of curved surfaces in computer graphics, and the design of non-Euclidean games and puzzles. They also have applications in fields such as physics, engineering, and architecture.

4. How do we solve problems in non-Euclidean geometries?

Solving problems in non-Euclidean geometries requires a different approach compared to Euclidean geometry. Instead of relying on traditional rules and theorems, we must understand the specific concepts and rules of the non-Euclidean geometry being studied. This may involve using different formulas and methods of proof.

5. Can non-Euclidean geometries exist in our physical world?

Non-Euclidean geometries can exist in our physical world, as seen in the study of curved spaces in general relativity. However, our physical world is often described by Euclidean geometry, so non-Euclidean geometries may not be as intuitive to us. It is important to note that both Euclidean and non-Euclidean geometries are useful and valid ways of understanding the world around us.

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