Download Math 310 Basic notions of geometry B. Noble Directions: Read the

Math 310 Basic notions of geometry
B. Noble
Directions: Read the section of your textbook and answer the following questions from the text. Include an illustration along with any definitions.
1. What are three undefined terms in geometry? Why are they undefined?
2. A line is determined by...
This means that only one line can possibly be made given...
3. def. Collinear points:
4. Give an example of betweenness:
5. def. Line segment:
6. def. Ray:
A plane has no thickness and it extends indefinitely in two directions. It is helpful to think of a plane like a
sheet of paper because a sheet of paper has very little thickness.
7. a. A plane is determined by...
b. Why do you think that all the points must be noncollinear? Think about how many planes you could get if
you picked collinear points.
8. def. coplanar:
9. def. noncoplanar:
10. def. skew lines:
11. def. intersecting lines:
12. def. concurrent lines:
13. def. parallel lines:
14. Can skew lines be parallel? Why?
Notice that on page 575 the text says, ”We assume the following properties of points, lines, and planes”. These
properties are axioms–taken to be self-evident–and are not proven (in fact, they are not provable!). You may
want to take a moment to reflect that any system for reasoning must have a foundation somewhere. These
are some of the basic ”building blocks” for geometry. What assumptions about life do you have that shape way
you live your life? (Don’t answer this on the paper–this is just something for you to think about on your own time.)
15. When is an angle formed?
Draw a diagram of an angle identifying the sides and the vertex. Due to the definition of an angle, you should
have at least three points on your angle.
16. An angle is measured according to the amount of ”opening” between its sides (unless specified otherwise, we
measure the smaller of the two openings). What type of measurement is commonly used to measure angles?
17. 1 degree=(how many) minutes
1 minute=(how many) seconds
18. Try EXAMPLE 9-1 on page 580. We’ll go over this.
19. List and define the types of angles listed on page 581 (acute, right, obtuse, straight).
20. def. Perpendicular Lines:
21. Using your protractor and straight edge, draw an angle with a measure of 55◦ , 155◦ .
22. Perform each of the following operations. Leave your answers in simplest form:
a. 27◦ 460 2200 + 88◦ 240 5000
b. 105◦ 480 2400 − 15◦ 550 3400
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