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Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell

Chapter 1

Basics of Geometry

Educators


Problem 1

Compare collinear points and coplanar points.

Luca A.
Numerade Educator

Problem 2

Which term does not belong with the other three? Explain your reasoning.
$\overline{\mathrm{AB}}$
plane CDE
FG
HI

Sachit K.
Numerade Educator

Problem 3

In Exercises $3-6,$ use the diagram.

Name four points.

Luca A.
Numerade Educator

Problem 4

In Exercises $3-6,$ use the diagram.

Name two lines.

Sachit K.
Numerade Educator

Problem 5

In Exercises $3-6,$ use the diagram.

Name the plane that contains points $A, B,$ and $C$

Luca A.
Numerade Educator

Problem 6

In Exercises $3-6,$ use the diagram.

Name the plane that contains points $A, D,$ and $E$

Sachit K.
Numerade Educator

Problem 7

In Exercises $7-10,$ use the diagram.

Give two other names for $\overline{\mathrm{WQ}}$

Luca A.
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Problem 8

In Exercises $7-10,$ use the diagram.

Give another name for plane $\mathrm{V}$

Sachit K.
Numerade Educator

Problem 9

In Exercises $7-10,$ use the diagram.

Name three points that are collinear. Then name a fourth point that is not collinear with these three points.

Luca A.
Numerade Educator

Problem 10

In Exercises $7-10,$ use the diagram.

Name a point that is not coplanar with $\mathrm{R}, \mathrm{S},$ and $\mathrm{T}$ .

Sachit K.
Numerade Educator

Problem 11

In Exercises $11-16,$ use the diagram.

What is another name for $\overline{\mathrm{BD}} ?$

Luca A.
Numerade Educator

Problem 12

In Exercises $11-16,$ use the diagram.

What is another name for $\overline{\mathrm{AC}}$ ?

Sachit K.
Numerade Educator

Problem 13

In Exercises $11-16,$ use the diagram.

What is another name for ray $\mathrm{AE}$ ?

Luca A.
Numerade Educator

Problem 14

In Exercises $11-16,$ use the diagram.

Name all rays with endpoint E.

Sachit K.
Numerade Educator

Problem 15

In Exercises $11-16,$ use the diagram.

Name two pairs of opposite rays.

Luca A.
Numerade Educator

Problem 16

In Exercises $11-16,$ use the diagram.

Name one pair of rays that are not opposite rays.

Sachit K.
Numerade Educator

Problem 17

In Exercises $17-24,$ sketch the figure described.

plane $\mathrm{P}$ and line $\ell$ intersecting at one point

Luca A.
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Problem 18

In Exercises $17-24,$ sketch the figure described.

plane $\mathrm{K}$ and line $\mathrm{m}$ intersecting at all points on line m

Sachit K.
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Problem 19

In Exercises $17-24,$ sketch the figure described.

$A B$ and $A C$

Luca A.
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Problem 20

In Exercises $17-24,$ sketch the figure described.

$\mathrm{MN}$ and $\mathrm{NX}$

Sachit K.
Numerade Educator

Problem 21

In Exercises $17-24,$ sketch the figure described.

plane M and $\mathrm{NB}$ intersecting at $\mathrm{B}$

Luca A.
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Problem 22

In Exercises $17-24,$ sketch the figure described.

plane M and $\mathrm{NB}$ intersecting at $\mathrm{A}$

Sachit K.
Numerade Educator

Problem 23

In Exercises $17-24,$ sketch the figure described.

plane $\mathrm{A}$ and plane $\mathrm{B}$ not intersecting

Luca A.
Numerade Educator

Problem 24

In Exercises $17-24,$ sketch the figure described.

plane $\mathrm{C}$ and plane $\mathrm{D}$ intersecting at $\mathrm{XY}$

Sachit K.
Numerade Educator

Problem 25

In Exercises 25 and 26, describe and correct the error in naming opposite rays in the diagram.

ADand ACare opposite rays.

Luca A.
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Problem 26

In Exercises 25 and 26, describe and correct the error in naming opposite rays in the diagram.

$\overline{\mathrm{YC}} \mathrm{and}$ $\overline{\mathrm{YE}}$ are opposite rays.

Sachit K.
Numerade Educator

Problem 27

In Exercises $27-34,$ use the diagram.

Name a point that is collinear with points $\mathrm{E}$ and $\mathrm{H}$ .

Luca A.
Numerade Educator

Problem 28

In Exercises $27-34,$ use the diagram.

Name a point that is collinear with points $\mathrm{B}$ and $\mathrm{I}$

Sachit K.
Numerade Educator

Problem 29

In Exercises $27-34,$ use the diagram.

Name a point that is not collinear with points $\mathrm{E}$
and $\mathrm{H}$ .

Luca A.
Numerade Educator

Problem 30

In Exercises $27-34,$ use the diagram.

Name a point that is not collinear with points $\mathrm{B}$ and $\mathrm{I}$ .

Sachit K.
Numerade Educator

Problem 31

In Exercises $27-34,$ use the diagram.

Name a point that is coplanar with points $\mathrm{D}, \mathrm{A},$ and $\mathrm{B}$ .

Luca A.
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Problem 32

In Exercises $27-34,$ use the diagram.

Name a point that is coplanar with points $\mathrm{C}, \mathrm{G},$ and $\mathrm{F}$

Sachit K.
Numerade Educator

Problem 33

In Exercises $27-34,$ use the diagram.

Name the intersection of plane AEH and plane FBE.

Luca A.
Numerade Educator

Problem 34

In Exercises $27-34,$ use the diagram.

Name the intersection of plane BGF and plane HDG.

Sachit K.
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Problem 35

In Exercises $35-38,$ name the geometric term modeled by the object.

Luca A.
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Problem 36

In Exercises $35-38,$ name the geometric term modeled by the object.

Sachit K.
Numerade Educator

Problem 37

In Exercises $35-38,$ name the geometric term modeled by the object.

Luca A.
Numerade Educator

Problem 38

In Exercises $35-38,$ name the geometric term modeled by the object.

Sachit K.
Numerade Educator

Problem 39

In Exercises $39-44,$ use the diagram to name all the points that are not coplanar with the given points.

$\mathrm{N}, \mathrm{K},$ and $\mathrm{L}$

Luca A.
Numerade Educator

Problem 40

In Exercises $39-44,$ use the diagram to name all the points that are not coplanar with the given points.

$\mathrm{P}, \mathrm{Q},$ and $\mathrm{N}$

Sachit K.
Numerade Educator

Problem 41

In Exercises $39-44,$ use the diagram to name all the points that are not coplanar with the given points.

$P, Q,$ and $R$

Luca A.
Numerade Educator

Problem 42

In Exercises $39-44,$ use the diagram to name all the points that are not coplanar with the given points.

$\mathrm{R}, \mathrm{K},$ and $\mathrm{N}$

Sachit K.
Numerade Educator

Problem 43

In Exercises $39-44,$ use the diagram to name all the points that are not coplanar with the given points.

$\mathrm{P}, \mathrm{S},$ and $\mathrm{K}$

Luca A.
Numerade Educator

Problem 44

In Exercises $39-44,$ use the diagram to name all the points that are not coplanar with the given points.

$\mathrm{Q}, \mathrm{K},$ and $\mathrm{L}$

Sachit K.
Numerade Educator

Problem 45

Given two points on a line and a third point not on the line, is it possible to draw a plane that includes the line and the third point? Explain your reasoning.

Luca A.
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Problem 46

Is it possible for one point to be in two different planes? Explain your reasoning.

Sachit K.
Numerade Educator

Problem 47

Explain why a four-legged chair may rock from side to side even if the floor is level. Would a three-legged chair on the same level floor rock from side to side? Why or why not?

Luca A.
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Problem 48

You are designing the living room of an apartment. Counting the floor, walls, and ceiling, you want the design to contain at least eight different planes. Draw a diagram of your design. Label each plane in your design.

Sachit K.
Numerade Educator

Problem 49

Two coplanar intersecting lines will always intersect at one point. What is the greatest number of intersection points that exist if you draw four coplanar lines? Explain.

Luca A.
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Problem 50

You and your friend walk in opposite directions, forming opposite rays. You were originally on the corner of Apple Avenue and Cherry Court.
a. Name two possibilities of the road and direction you and your friend may have traveled.
b. Your friend claims he went north on Cherry Court, and you went east on Apple Avenue. Make an argument as to why you know this could not have happened.

Sachit K.
Numerade Educator

Problem 51

In Exercises $51-54$ graph the inequality on a number line. Tell whether the graph is a segment, a ray or rays, a point, or a line.

$$x \leq 3$$

Luca A.
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Problem 52

In Exercises $51-54$ graph the inequality on a number line. Tell whether the graph is a segment, a ray or rays, a point, or a line.

$$-7 \leq x \leq 4$$

Sachit K.
Numerade Educator

Problem 53

In Exercises $51-54$ graph the inequality on a number line. Tell whether the graph is a segment, a ray or rays, a point, or a line.

$$x \geq 5 \text { or } x \leq-2$$

Luca A.
Numerade Educator

Problem 54

In Exercises $51-54$ graph the inequality on a number line. Tell whether the graph is a segment, a ray or rays, a point, or a line.

$$\left.\right|_{\mathrm{X}} | \leq 0$$

Sachit K.
Numerade Educator

Problem 55

Use the diagram.
a. Name two points that are collinear with $\mathrm{P}$ .
b. Name two planes that contain J.
c. Name all the points that are in more than one plane.

Luca A.
Numerade Educator

Problem 56

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

A line ______ has endpoints.

Sachit K.
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Problem 57

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

A line and a point ________ intersect.

Luca A.
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Problem 58

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

A plane and a point ________ intersect.

Sachit K.
Numerade Educator

Problem 59

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

Two planes ________ determine a line.

Luca A.
Numerade Educator

Problem 60

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

Two points ________ determine a line.

Sachit K.
Numerade Educator

Problem 61

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

Any three points _____ determine a plane.

Luca A.
Numerade Educator

Problem 62

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

Any three points not on the same line ________ determine a plane.

Sachit K.
Numerade Educator

Problem 63

In Exercises $56-63,$ complete the statement with always, sometimes, or never. Explain your reasoning.

Two lines that are not parallel _________ intersect.

Luca A.
Numerade Educator

Problem 64

Is it possible for three planes to never intersect? intersect in one line? intersect in one point? Sketch the possible situations.

Sachit K.
Numerade Educator

Problem 65

Find the absolute value.

$|6 2 |$

Luca A.
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Problem 66

Find the absolute value.

$$|3-9|$$

Sachit K.
Numerade Educator

Problem 67

Find the absolute value.

$$|-8-2|$$

Luca A.
Numerade Educator

Problem 68

Find the absolute value.

$$|7-11|$$

Sachit K.
Numerade Educator

Problem 69

Solve the equation.

$$18 \mathrm{x}=43$$

Luca A.
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Problem 70

Solve the equation.

$$36 \mathrm{x}=20$$

Sachit K.
Numerade Educator

Problem 71

Solve the equation.

$$x-15=7$$

Luca A.
Numerade Educator

Problem 72

Solve the equation.

$$x-23=19$$

Sachit K.
Numerade Educator