## 2016 - 2017 Fall Semester MATH 3110 College Geometry (Barsamian) Final Exam Information

• The exam is on Friday, December 9, from 10:10am to 12:10pm in Morton 313
• You may use your packet "Definitions and Theorems" for reference.
• The Exam is 8 problems.

1. Prove a Theorem from Chapter 5 Plane Separation. (I choose the theorem.)
• Theorem 27 each half-plane contains three non-collinear points. (Ch. 4, p. 114)
• Theorem 28 Pasch's Theorem about a line intersecting a side of a triangle between vertices. (Ch. 4, p. 116)
• Theorem 29 about a line intersecting two sides of a triangle between vertices. (Ch. 4, p. 94)
• Theorem 33 Points on a side of a triangle are in the interior of the opposite angle. (Ch. 4, p. 116)
• Theorem 35 The Crossbar Theorem (Ch. 4, p. 120)
2. Prove a Theorem involving concurrence of three lines associated to triangles. It will be one of these. (I choose the theorem.) (You might have to prove, or you might have to just justify and illustrate. And you might have to do the whole proof, or you might just have to do part of the proof.)
• Theorem 92 about the concurrence of the three angle bisectors for triangles in Neutral Geometry. (Ch. 8, p. 194))
• Theorem 95 about the existence of an inscribed circle for triangles in Neutral Geometry. (Ch. 8, p. 196)
• Theorem 106 about the concurrence of perpendicular bisectors of the sides for triangles in Euclidean Geometry. (Ch. 9, p. 206)
• Theorem 107 In Euclidean Geometry, every triangle can be circumscribed. (Ch. 9, p. 207)
• Theorem 113 about the concurrence of the altitudes for triangles in Euclidean Geometry. (Ch. 9, p. 211)

3. Solve a Geometric Problem Involving Triangles. (I choose one.)
• Chapter 10 Exercises (p. 231 - 234) ,,
• Chapter 11 Exercises (p. 250 - 254) ,,,,

4. Solve a Geometric Problem Involving Circles. (I choose one.)
• Chapter 8 Exercises (p. 197 - 199) ,,,,
• Chapter 12 Exercises (p. 274 - 277) ,,,

5. Prove a Theorem that has a proof involving creating a triangle inside or adjacent to an existing triangle. (I choose the theorem.)
• Theorem 59 The Neutral Geometry Exterior Angle Theorem. (Ch. 7, p. 162)
• Theorem 61 BS ==> BA. (Ch. 7, p. 164)
• Theorem 64 The Triangle Inequality for Neutral Geometry. (Ch. 7, p. 165)
• Theorem 110 The Triangle Midsegment Theorem. (Ch. 9, p. 209)
• Theorem 122 The Angle Bisector Theorem Theorem. (Ch. 10, p. 222)

6. Prove a Theorem that I proved with an indirect proof in the book. (I choose one theorem.)
• Theorem 62 BA ==> BS (Ch. 7, p. 164)
• Theorem 74 Alternate Interior Angle Theorem (Ch. 7, p. 180)
• Theorem 99 about parallel lines, transversals, and the special angle property in Euclidean Geometry. (Ch. 9, p. 203)

7. Prove a Theorem that is stated as an Equivalence Theorem. (I choose the theorem, and which part you will prove.) (You won't have to prove all the parts.)
• Theorem 73 about angles formed by two lines and a transversal in Neutral Geometry (Chapter 7, p. 178)
• Theorem 85 about special rays in isosceles triangles (Ch. 8, p. 191)
• Theorem 86 about points equidistant from the endpoints of a line segment. (Ch. 8, p. 192)