Lesson
2:
Points, Lines, and Planes
uses kno\nn words to describe a new
1) Point -
2) Line -
has no dimension, represented by a small dot and labeled
in both directions
extends in two dimensions, represented by a shape similar to a slanted tabletop extending forever
in all directions
f
ornk
+l^'* lit ø *lt"
)+J lie
P,^E
1)
with a capital letter
extends in one dimension, represented by a straight line with two arrows to show continuing forever
3) Plane -
Ex
word
sa*t<- I '\*e-
t'v1
a. Name 3 collinear points
b. Name 4 coplanar points
c. Name
Poìats
3 noncollinear points
lltl
a'cc e"ltAt"î
ìnter,'oc
o4 z Pls
s
Consider line AB.
I.B-
i,
all points between A and g onl-B>
s
AB is the initial point A and all points on AB on the same side of A
Be very careful in labeling.
<â
Aß
AB
A8
as point B
If C is betweenpoints A and B, then we call
C?un¿d
Ex 1) Draw 4 noncollinear points M, N, O, P. Then
¿ru*ffi, õì, **, *¿ ffi
+>
Ex2) Given EH, name two pairs of opposite rays.
-+ +
Fc'
Are GF and GE the same ray?
ÍE
EF
-Ð
Gfr, 6F
(c
c7)
/es
having one or more poi
Sketch the following:
l)
s
n^
line AB and a plane that do not intersect
9o
:
2) two
planes that do not intersect and a line that
€
3) a line BC intersecting
4) a line intersecting
a plane at one
a plane at
point B
infinite points
5) Three points that are coplanar but not col
6) Two lines that intersect in a point
each plane at exactly one point
H
and all lie in the same plane
7) two planes that intersect at linelÈ
(ry"'':,(e)
-r-
â_t
Lesson 2 Practice: Points, Lines, and Planes
1. Who is considered the Father of Geometry?
2. lVhat were his three
undefined terms?
a. ?t;nl
b.
3. How can you prove a conjecture
4. How
Lln-
c. Pl*.
false?
can you prove a conjecture true?
Determine if each statement is true or false.
F
5. Points A
F
6. Points A, B, and C are collinear.
and B are collinear.
F
7. Points D and E are collinear.
F
8. Points
J and
9. Points
J, K, and
T
10. Points J, K, and L are coplanar.
F
I
F
12. Points L, M, and N are coplanar.
l. Points J, K, and M are coplanar.
13. Points J, K, L, and M are coplanar.
A, B, and
C
15. D, C, and H
16. F, A, and
E
17. E,F, and G
18. A, B, and
H
19. B, C, and F
ê
20. AB and BC intersect at
ê
C
oE
L are collinear.
Name a point that is coplanar with the given points.
14.
B
K are collinear.
F
T
oD
ê
21. AD and AE intersect at
ë
22. Plane ABC and plane DCG intersect
at
23. Plane EAD and plane BCD intersect
at
DC
K
L
a
Sketch the figure described.
24. Drawtwo points, X
and
Y.
Then
sketch*?. Add a point
rW
between X and Y so that
Wk*¿ lfù*.
opposite rays.
lrl/
m
25. Two lines that lie in a plane but do not intersect.
26. Two lines that intersect
27. Two rays that
28. Two
and another line that does not intersect either one.
are coplanar but not collinear.
planes that intersect at
linelÑ.
29. Threeplanes that intersect at linefÈ.
30. Points K, L, M, and N are not coplanar. What is the intersection-g
A.Kandl
B.MandN
KLM
and plane KLN?
C.KL
l0