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CHAPTER 1 
Tools of Geometry
SECTION 1-1 
Points, Lines, and Planes
ESSENTIAL QUESTIONS 
How do you identify and model points, lines, and 
planes? 
How do you identify intersecting lines and planes?
VOCABULARY 
1. Undefined Term: 
2. Point: 
3. Line:
VOCABULARY 
1. U n d e fi n e d T e r m : The things in Geometry that can 
really only be explained in examples and 
descriptions 
2. Point: 
3. Line:
VOCABULARY 
1. U n d e fi n e d T e r m : The things in Geometry that can 
really only be explained in examples and 
descriptions 
2. P o i n t : A location in space with no shape or size; 
noted as a capital letter 
3. Line:
VOCABULARY 
1. U n d e fi n e d T e r m : The things in Geometry that can 
really only be explained in examples and 
descriptions 
2. P o i n t : A location in space with no shape or size; 
noted as a capital letter 
3. L i n e : 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
VOCABULARY 
4. Plane: 
5. Collinear: 
6. Coplanar: 
7. Intersection:
VOCABULARY 
4. P l a n e : 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:
VOCABULARY 
4. P l a n e : 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. C o l l i n e a r : Points that lie on the same line 
6. Coplanar: 
7. Intersection:
VOCABULARY 
4. P l a n e : 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. C o l l i n e a r : Points that lie on the same line 
6. C o p l a n a r : Points that lie in the same plane 
7. Intersection:
VOCABULARY 
4. P l a n e : 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. C o l l i n e a r : Points that lie on the same line 
6. C o p l a n a r : Points that lie in the same plane 
7. I n t e r s e c t i o n : Where two figures meet; this is the set 
of points they have in common
VOCABULARY 
8. Definition: 
9. Defined Terms: 
10. Space:
VOCABULARY 
8. D e fi n i t i o n : Explanations that are used based off of 
other undefined and defined terms 
9. Defined Terms: 
10. Space:
VOCABULARY 
8. D e fi n i t i o n : Explanations that are used based off of 
other undefined and defined terms 
9. D e fi n e d T e r m s : Another way of working with a 
definition 
10. S p a c e : An infinite three-dimensional set of points
EXAMPLE 1 
Use the figure to name each of the following. 
a. A line containing point R 
b. A plane containing point P
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
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
EXAMPLE 2 
Name the geometric shape modeled by each object. 
a. A crack in a sidewalk 
b. A drop of water on the sidewalk
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
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
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.
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
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.
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.
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
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
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
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
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
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?
PROBLEM SET
PROBLEM SET 
p. 8 #1-47 odd, 58 
“In terms of being late or not starting at all, then it’s 
never too late.” - Alison Headley

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Geometry Section 1-1 1112

  • 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. U n d e fi n e d T e r m : The things in Geometry that can really only be explained in examples and descriptions 2. Point: 3. Line:
  • 6. VOCABULARY 1. U n d e fi n e d T e r m : The things in Geometry that can really only be explained in examples and descriptions 2. P o i n t : A location in space with no shape or size; noted as a capital letter 3. Line:
  • 7. VOCABULARY 1. U n d e fi n e d T e r m : The things in Geometry that can really only be explained in examples and descriptions 2. P o i n t : A location in space with no shape or size; noted as a capital letter 3. L i n e : 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. P l a n e : 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. P l a n e : 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. C o l l i n e a r : Points that lie on the same line 6. Coplanar: 7. Intersection:
  • 11. VOCABULARY 4. P l a n e : 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. C o l l i n e a r : Points that lie on the same line 6. C o p l a n a r : Points that lie in the same plane 7. Intersection:
  • 12. VOCABULARY 4. P l a n e : 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. C o l l i n e a r : Points that lie on the same line 6. C o p l a n a r : Points that lie in the same plane 7. I n t e r s e c t i o n : 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. D e fi n i t i o n : Explanations that are used based off of other undefined and defined terms 9. Defined Terms: 10. Space:
  • 15. VOCABULARY 8. D e fi n i t i o n : Explanations that are used based off of other undefined and defined terms 9. D e fi n e d T e r m s : Another way of working with a definition 10. S p a c e : 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?
  • 33. PROBLEM SET p. 8 #1-47 odd, 58 “In terms of being late or not starting at all, then it’s never too late.” - Alison Headley