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

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