11. Will every ray contain a line segment? Why or why not? What kind of reasoning is used to arrive at this conclusion?

12. If I have two lines, will they cross? Explain fully. What postulate supports your answer to this question?

13. If I have a line segment, and another point not on the line segment, how many different geometric elements might I also have? What are those elements? What kind of reasoning did you use?

For Questions 14-16: Imagine you have been called as a expert witness in a court case. Your expertise is in the area of planes (not airplanes, just planes in geometry). Your task is to convince the jury that there is, in fact, a plane based on the given information. You must prove all three of the definitions of a plane given in Lesson 1. You may need to include some other definitions such as the definition of an angle, a ray, etc.

A plane is defined by any of the following:

• three points that are not collinear (Ex: points U, B, and E)
• a line and a point not lying on the line(Ex: ln_UH and point E)
• two lines which intersect in a single point or are parallel (Ex: ln_BH and ln_EB intersect at a single point B)

Question from the lawyer: "Dr. Expert, I only seea 70 anglehere, Exhibit A. Kelly said that having this angle means you have a plane. From what I see, none of the definition of a plane say that an angle defines a plane. Explain how each definition proves that an angle defines a plane."

Exhibit A:

State the definition and then explain how you can prove each definition given the angle.

14. Definition 1:

Proof:

15. Definition 2:

Proof:

16. Definition 3:

Proof: