I will have a presentation on elementary geometry, and more precisely on the straight line and the triangle.
The presentation should be in the university, in front of the fellow students.
For this I use the book "Elementary Geometry" by Ilka Agricola, Thomas Friedrich (chapters 1.1 and 1.2).
The following topics are discussed there with regard to the straight line:
- Intercept theorem
- Pappus's hexagon theorem
- Desargues's theorem
- Theorem of Thales
And regarding the triangle:
- Theorem: A triangle is isosceles if and only if two of its inner angles are equal.
- Theorem: A triangle is equilateral if and only if its three interior angles are equal.
- Exterior angle theorem
- Sum of angles in a triangle
- Alternate angle theorem
So would the structure of the presentation mention all of these topics and prove some of them? Or what do you think?
Obviously, this depends on your presentation and the rules.
However, examples always help in math. Explain it, show the equation, then give an example, preferably visual. Especially for geometry, make things visual. It's way easier to show things than just talk about it.
About your question about more emphasis on specific questions, it really depends on what the rules are. If I were you I would go over theorems that you feel are more special or useful. Prove the important ones, depending on how much time you have.
-FruDe