Review the following concept if necessary: The Basic Building Blocks of Geometry Study Guide.

**The Basic Building Blocks Of Geometry Practice Questions**

**Problems**

- Are there more points on than point
*A*and point*B*? - How are points distinguished from one another?
- Why would lines, segments, rays, or planes not exist if points do not exist?
- Write six different names for this line.
- How many points are on a line?
- Why do you think the notation for a line has two arrowheads?

- Name two different rays with endpoint S.
- Why is it important to name the endpoint of a ray first?
- Why are ray and ray not the same?
- Name six different line segments shown.
- Why are arrowheads not included in line segment notation?
- How many points are on a line segment?

- A line is different from a ray because _____.
- A property of a point is _____.
- A ray is different from a segment because _____.
- A property of a line segment is _____.
- A plane is different from a line because _____.

- What are three examples of figures that occur in space?
- Can three points be noncollinear? Why or why not?
- Can coplanar points be noncollinear? Why or why not?
- Can collinear points be coplanar? Why or why not?

### Practice

Problems 22 - 25, please refer to the following geometric figure. State whether each set of points is collinear.

*A, B, C**A, E, F**B, D, F**A, E**A, B, C, E**D, B, C, E**B, C, E, F**A, B, E*

Problems 26 - 29, please refer to the following geometric figure. Determine whether each set of points is coplanar.

Determine whether the following statements are true or false.

- and are the same line.
- and are the same ray.
- and are the same segment.
- Any four points
*W, X, Y*, and*Z*must lie in exactly one plane.

Draw and label a figure for the following two questions to fit each description, if possible. Otherwise, state "not possible."

- four collinear points
- three noncoplanar points
- Are three points that are collinear
*sometimes, always*, or*never*coplanar?

**Answers**

- Yes; there are countless points on any line.
- Points are distinguished from one another by the names assigned to them:
*A, B, C*, and so on. - Lines, segments, rays, and planes are made up of a series of points.
- An infinite number of points are on a line.
- The notation for a line has two arrowheads because a line extends forever in both directions.
- The endpoint is the beginning of a ray.
- They are different because they have different endpoints and extend in different directions.
- Line segments do not extend indefinitely. They have starting points and stopping points.
- An infinite number of points are on a line segment.
- A line has no endpoints; a ray has one endpoint.
- A point has no size, has no dimension, indicates a definite location, and is named with an italicized capital letter.
- A ray extends indefinitely in one direction, but a segment has two endpoints.
- A line segment is part of a line, has endpoints, includes an infinite set of points, and is one dimensional.
- A plane has two dimensions; a line has one dimension.
- Answers will vary but could include a sphere, cube, rectangular prism, or triangular prism.
- Yes, a third point could be off the line.
- Yes, coplanar points can be noncollinear because two points could be on one line with a third point that lies the same plane but not on the same line.
- Yes, collinear points must be coplanar because if a line is in a plane, then all points on that line are in the same plane.
- yes
- no
- yes
- Yes; remember that any two points determine a line, even if it is not drawn.
- yes
- no
- no
- Yes; remember that any three noncollinear points determine a plane, even if it is not drawn.
- true
- false
- true
- False; sometimes they do, but not always.
- Not possible; any three points are coplanar.
- always

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