This document introduces basic geometry concepts such as points, lines, planes, and their intersections. It defines a point as having no size or shape, a line as an infinite set of collinear points, and a plane as a flat surface extending indefinitely. Examples demonstrate identifying geometric shapes from real-world objects and graphing points and lines on a coordinate plane. The summary defines key terms and provides examples of geometric concepts and relationships.

1. CHAPTER 1
Tools of Geometry

2. SECTION 1-1
Points, Lines, and Planes

3. ESSENTIAL QUESTIONS
How do you identify and model points, lines, and
planes?
How do you identify intersecting lines and planes?

4. VOCABULARY
1. Undefined Term:
2. Point:
3. Line:

5. VOCABULARY
1. Undefined Term: The things in Geometry that can
really only be explained in examples and
descriptions
2. Point:
3. Line:

6. VOCABULARY
1. Undefined Term: The things in Geometry that can
really only be explained in examples and
descriptions
2. Point: A location in space with no shape or size;
noted as a capital letter
3. Line:

7. VOCABULARY
1. Undefined Term: The things in Geometry that can
really only be explained in examples and
descriptions
2. Point: A location in space with no shape or size;
noted as a capital letter
3. Line: An infinite number of points that together have
no thickness or width; need two points to determine
the line; use either a lowercase letter or AB

8. VOCABULARY
4. Plane:
5. Collinear:
6. Coplanar:
7. Intersection:

9. VOCABULARY
4. Plane: A flat surface with at least three points that
goes on forever in all directions; three points
determine a plane; Often a capital script letter
5. Collinear:
6. Coplanar:
7. Intersection:

10. VOCABULARY
4. Plane: A flat surface with at least three points that
goes on forever in all directions; three points
determine a plane; Often a capital script letter
5. Collinear: Points that lie on the same line
6. Coplanar:
7. Intersection:

11. VOCABULARY
4. Plane: A flat surface with at least three points that
goes on forever in all directions; three points
determine a plane; Often a capital script letter
5. Collinear: Points that lie on the same line
6. Coplanar: Points that lie in the same plane
7. Intersection:

12. VOCABULARY
4. Plane: A flat surface with at least three points that
goes on forever in all directions; three points
determine a plane; Often a capital script letter
5. Collinear: Points that lie on the same line
6. Coplanar: Points that lie in the same plane
7. Intersection: Where two figures meet; this is the set
of points they have in common

13. VOCABULARY
8. Definition:
9. Defined Terms:
10. Space:

14. VOCABULARY
8. Definition: Explanations that are used based off of
other undefined and defined terms
9. Defined Terms:
10. Space:

15. VOCABULARY
8. Definition: Explanations that are used based off of
other undefined and defined terms
9. Defined Terms: Another way of working with a
definition
10. Space: An infinite three-dimensional set of points

16. EXAMPLE 1
Use the figure to name each of the following.
a. A line containing point R
b. A plane containing point P

17. EXAMPLE 1
Use the figure to name each of the following.
a. A line containing point R
m, RT, RS, etc.
b. A plane containing point P

18. EXAMPLE 1
Use the figure to name each of the following.
a. A line containing point R
m, RT, RS, etc.
b. A plane containing point P
A

19. EXAMPLE 2
Name the geometric shape modeled by each object.
a. A crack in a sidewalk
b. A drop of water on the sidewalk

20. EXAMPLE 2
Name the geometric shape modeled by each object.
a. A crack in a sidewalk
line
b. A drop of water on the sidewalk

21. EXAMPLE 2
Name the geometric shape modeled by each object.
a. A crack in a sidewalk
line
b. A drop of water on the sidewalk
point

22. EXAMPLE 3
Draw and label plane T that contains lines UV and
WX such that the lines intersect at point Z. Then,
add a point H to plane T so that it is not collinear
with either UV or WX.

23. EXAMPLE 3
Draw and label plane T that contains lines UV and
WX such that the lines intersect at point Z. Then,
add a point H to plane T so that it is not collinear
with either UV or WX.
Compare your drawings with a neighbor; discuss

24. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.

25. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.

26. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.
x
y

27. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.
x
y
A

28. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.
x
y
A
B

29. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.
x
y
A
B

30. EXAMPLE 4
Points A(−3, 3) and B(2, −5) form a line. Graph the
points and line on the coordinate plane, then add a
point C so that it is collinear with A and B.
x
y
A
B
C

31. EXAMPLE 5
Answer the following.
a. How many points are need to form a line?
b. How many points are needed to form a plane?
c. What is the intersection of two planes?
d. What is the intersection of two lines?
e. What is the difference between collinear and coplanar?