Idea Transcript
Name LESSON
1-1
Date
Class
Practice B Understanding Points, Lines, and Planes
Use the figure for Exercises 1–7. 1. Name a plane. 2. 3.
Possible_ answers: plane BCD; plane BED _ _
_
or CE Name a segment. BD , BC , BE ,__ ‹ › ‹___› ‹__› Name a line. Possible answers: EC ; BC ; BE
# "
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4. Name three collinear points.
points B, C, and E $
5. Name three noncollinear points.
Possible answers: points B, C, and D or points B, E, and D 6. Name the intersection of a line and a segment not on the line.
___›
point B
___›
BC and BE
7. Name a pair of opposite rays. Use the figure for Exercises 8–11.
M
8. Name the points that determine plane R.
points X, Y, and Z
9. Name the point at which line m intersects
:
point Z
plane R.
7
10. Name two lines in plane R that intersect line m. ‹__› ‹__›
XZ and YZ
11. Name a line in plane R that does not intersect
8
9
‹__›
line m.
XY
Draw your answers in the space provided. Michelle Kwan won a bronze medal in figure skating at the 2002 Salt Lake City Winter Olympic Games. 12. Michelle skates straight ahead from point L and stops at point M. Draw her path. 13. Michelle skates straight ahead from point L and continues through point M. Name a figure that represents her path. Draw her path. 14. Michelle and her friend Alexei start back to back at point L and skate in opposite directions. Michelle skates through point M, and Alexei skates through point K. Draw their paths. Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Holt Geometry
Name LESSON
1-1
Date
Class
Name
Date
Class
Practice B 1-1 Understanding Points, Lines, and Planes
Practice A
LESSON
Understanding Points, Lines, and Planes
Use the figure for Exercises 1–7.
Use the figure for Exercises 1–3. ‹__›
1. Name a plane.
1. Name two points that determine line AC.
point A and point C
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2. Name a point that is NOT collinear with point A and point C.
line
�
�
�
5. Name three noncollinear points.
Possible answers: points B, C, and D or points B, E, and D ___›
.
point B
___›
BC and BE
7. Name a pair of opposite rays.
.
plane
7. Coplanar points lie in the same
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6. Name the intersection of a line and a segment not on the line.
plane
6. Three noncollinear points determine a
_
points B, C, and E
.
line
5. Collinear points lie on the same
_
BD, BC, BE,__ or CE ‹ › ‹___› ‹__› Name a line. Possible answers: EC ; BC ; BE
4. Name three collinear points.
�
point A, point B, and point C
3. Name the points that determine plane ABC. 4. Two points determine one
3.
�
point B
Possible_ answers: plane BCD; plane BED _
2. Name a segment.
�
Use the figure for Exercises 8–11.
.
�
8. Name the points that determine plane R.
points X, Y, and Z
Use the figure for Exercises 8–10. �
one
9. Find the number of endpoints of UV.
�
XZ and YZ
�
__›
XY
line m.
Draw your answers in the space provided.
�
�
�
�
Michelle Kwan won a bronze medal in figure skating at the 2002 Salt Lake City Winter Olympic Games.
�
12. Michelle skates straight ahead from point L and stops at point M. Draw her path.
_
12. Points P___and Q lie in a plane. Of PQ, ‹___› › PQ, or PQ, name the one that has no endpoints. __
13. Michelle skates straight ahead from point L and continues through point M. Name a figure that represents her path. Draw her path.
�
�
‹ ›
PQ
3
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Date
Class
Holt Geometry
LESSON
1-1
Understanding Points, Lines, and Planes
Use the figure for Exercises 1– 3.
A plane is named with three noncollinear points.
�
Characteristics
line
Possible answers: plane HIK; plane HJK; plane IJK
‹__› ‹__› ‹_› ‹__› ‹__›
‹_›
HI, HJ, IJ, IH, JH, and JI
line segment or segment
2 endpoints
ray
1 endpoint
plane
__›
ST and TS are not opposite rays because they do not have the same endpoint.
�
_
___›
ray RQ or RQ �
extends forever in all directions
plane FGH or plane V
� �
�
2. line MN
�
�
__›
4. EF
�
�
�
�
Name each figure using words and symbols.
8. Through any three points there is exactly one plane containing them.
5.
6.
Through any three noncollinear points there is exactly one plane containing them.
�
�
� �
9. If two planes intersect, then they intersect in exactly one plane.
___›
‹___›
ray ST or ST
line CD or CD
If two planes intersect, then they intersect in exactly one line.
7. Name the plane in two different ways.
Draw your answer in the space provided. 10. Window glass is transparent, so visible light passes through it. Imagine a double-paned window as two nonintersecting planes and sunlight as a line. Use sketches to show that a line contained in neither of the planes must intersect both or neither of the two planes.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
A ray is named starting with its endpoint.
�
�
_
point, line, plane
5
‹__›
�
3. JK
Postulates are basic true statements accepted without proof. Each statement below is incorrect. Rewrite each statement so that it is true.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Words and Symbols
�
•W
a line
7. Name three undefined terms in geometry.
•P point P
�
1. point W
__›
6. Imagine ST and TS drawn in the same plane. Taken together, what kind of figure do the rays form?
Holt Geometry
Draw and label a diagram for each figure.
5. Explain why ST and TS are or are not opposite rays. __›
Class
Diagram
extends forever in one direction
___›
___›
__›
�
segment XY or XY
has a finite length
and TS has its endpoint at T. ___›
Date
�
line AB or AB
extends forever in two directions
ST and TS are not the same figure because ST has its endpoint at S
___›
�
�
0 endpoints
2. Name the plane.
4. Explain why ST and TS are or are not the same figure.
�
Understanding Points, Lines, and Planes
�
__›
�
Reteach
Figure
�
�
3. Give six names for the line.
�
A point has no size. It is named using a capital letter. All the figures below contain points.
1. “This is plane HIJ.” Explain why this statement is incorrect.
H, I, and J are collinear.
4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Name
Practice C
___›
���
14. Michelle and her friend Alexei start back to back at point L and skate in opposite directions. Michelle skates through point M, and Alexei skates through point K. Draw their paths.
Name
___›
�
‹__›
point U
__›
�
11. Name a line in plane R that does not intersect
10. A ray is a part of a line that has one endpoint. Name the endpoint of UV.
1-1
�
10. Name two lines in plane R that intersect line m. ‹__› ‹__›
__›
LESSON
�
point Z
plane R.
point T and point U
11. A constellation is a group of stars that people use to make a picture. The seven _ stars_ make Big_Dipper. _the _ _ Draw_DE, FE, FG, GH, HI, JG, and JI to complete the picture.
�
9. Name the point at which line m intersects
8. A line segment is a part_ of a line and has two endpoints. Name the endpoints of TU.
8.
�
�
�
�
�
�
_
segment WX ; WX
plane LMN; plane Q
Holt Geometry
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Holt Geometry
Holt Geometry