Geometry Section 1-1 1112
33
CHAPTER 1 Tools of Geometry
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Transcript of Geometry Section 1-1 1112
CHAPTER 1Tools of Geometry
SECTION 1-1Points, Lines, and Planes
ESSENTIAL QUESTIONS
How do you identify and model points, lines, and planes?
How do you identify intersecting lines and planes?
VOCABULARY1. Undefined Term:
2. Point:
3. Line:
VOCABULARY1. Undefined Term: The things in Geometry that can
really only be explained in examples and descriptions
2. Point:
3. Line:
VOCABULARY1. 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:
VOCABULARY1. 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
VOCABULARY4. Plane:
5. Collinear:
6. Coplanar:
7. Intersection:
VOCABULARY4. 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:
VOCABULARY4. 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:
VOCABULARY4. 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:
VOCABULARY4. 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
VOCABULARY
8. Definition:
9. Defined Terms:
10. Space:
VOCABULARY
8. Definition: Explanations that are used based off of other undefined and defined terms
9. Defined Terms:
10. Space:
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
EXAMPLE 1Use the figure to name each of the following.
a. A line containing point R
b. A plane containing point P
EXAMPLE 1Use 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 1Use 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 2Name the geometric shape modeled by each object.
a. A crack in a sidewalk
b. A drop of water on the sidewalk
EXAMPLE 2Name the geometric shape modeled by each object.
a. A crack in a sidewalkline
b. A drop of water on the sidewalk
EXAMPLE 2Name the geometric shape modeled by each object.
a. A crack in a sidewalkline
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 4Points 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 4Points 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 4Points 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 4Points 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 4Points 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 4Points 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 4Points 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 5Answer 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
