Math 403: Euclidean Geometry
Midterm 1 - Review

Time & Location: Tuesday, Feb. 15, 10:00-10:50, 441 Altgeld.
Material: Sections 1.1-2.1 of the textbook. Also, Euclid's 5 axioms for geometry, especially the Parallel Postulate.

You should be prepared to state any of the following

Axioms:

• Axioms (A1)-(A4) for vector addition (the order is not important)
• Axioms (M1)-(M4) for scalar multiplication (the order is not important),
• The Dimension Axoim (D).

Definitions:

• Point P is on the line l_AB
• Line l₁ is parallel to line l₂
• Median of a triangle
• Centroid of a triangle or quadrilateral
• Weighted centroid of mass-points
• Barycentric coordinates
• Injective, surjective, bijective maps
• Translation τ_A
• Identity map
• Fixed point of a map

Results:

• Theorem of Ceva
• Theorem of Menelaus
• Theorem of Desargues
• Theorem of Pappus

In addition, you should be familiar with how to find the barycentric coordinates of a point P with respect to three points A, B, C. You should know how to convert between an equation (P-A)/(P-B) = r and an equation P = aA+bB.

Suggested Exercises: Try the odd-numbered exercises in Chapter 1, especially problems 1.9, 1.11, 1.15, 1.17, 1.23. Some of these were done in class, and they all have hints in the back of the book, but try to do them without consulting your notes or the back of the book. Another good thing to try is to look at some of the results in the text (like Theorem 1.4, for example) and try to prove them without looking at the proof in the book.