1
GEOMETRY PROJECT ON LESSON 1-2 DUE 9/7/10:
POINTS, LINES, AND PLANES
Student name : __________________
Period:______
EXERCISE I:
Refer to the diagram below
1)
a) Name line AB in another way
b) Give two other names for plane Q
1
2
c) Why is EBD not an acceptable name for plane Q?
2) Are the following sets of points collinear ?
a) E, B, and F
b) Line DB and line FC
c) Line AC and line ED
d) Line AE and line DC
e) F,
A,
B,
and C
f) F,
A, B, and D
g) Plane Q and line EC
h) Line FB and line BD
2
3
EXERCISE II:
Find the intersection of the following lines and planes in the figure above
a) Line GK and line LG
b) Planes GLM and LPN
d) Planes GHPN and KJP
e) Planes HJN and GKL
f) Line KP and plane KJN
g) Line KM and plane GHL
3
4
EXERCISE III:
Refer to the diagram above
a) Name plane P in another way
b) Name plane Q in another way
c) What is the intersection of planes P and Q?
d) Are A and C collinear?
e) Are D,A,B, and C coplanar?
f) Are D and C collinear?
g) What is the intersection of line AB and line DC
h) Are planes P and Q coplanar
i) Are line AB and plane Q coplanar?
j) Are B and C collinear?
4
5
EXERCICE IV: Points, Lines, and Planes
Use the figure below to answer questions 1- 6.
1)Name the plane with 3 letters: ______ (2) Line AC intersects the plane at what point? _____
3) Line HG and line GE intersect at what point? ____ (4) Name 3 collinear points: ______
5) Name a point NOT on the plane: _____ (6) Are points F, D, E and B coplanar? _____
EXERCISE V:
Use the figure above to answer questions 1-7.
1) How many planes are there in the figure? _____
2) How many planes contain H? ______
5
6
3) Name three collinear points: ______
4) Name two points not on the Plane XBN: _____
5) Name four points that are coplanar: _______
6) Name a line that does NOT contain J: ______
7) Name three non-collinear points: ______
EXERCISE VI:
Draw 
AB
EXERCISE VII: Draw 
, 
, and AC .Use a straightedge.
CD
AB
6
7
EXERCISE VIII:
Name a point that is collinear with the given points
_ B and E:
_ C and H:
_ D and G:
_ A and C:
_ H and E:
_ G and B:
EXERCISE IX:
Name a point that is coplanar with the given points
_ M, N, R:
_ M, N, O:
_ M, T, Q:
_ Q, T, R:
_ T, R, S:
_ Q, S, O:
7
8
EXERCISE X: Determine if the pairs of lines appear to be parallel, perpendicular, or skew. It’s OK to
write symbols for parallel and perpendicular.
a)Line BF and line AE are ________________ b)Line CG and line HG are ______________
c)Line AD and line AE are _______________
d) Line FG and line EH are ____________
e)Line AD and line HG are _______________ f) line HG and line BF are _______________
EXERCISE XI: Use the diagram below.
a. Name the intersection of line BE and line CD .
8
9
b. Name the intersection of line BE and plane A.
c. Name the intersection of line DB and plane F.
d. Name the intersection of plane A and F.
EXERCISE XII: Use the diagram below. Be sure to use correct notation.
a.
Name any four points.
b. Name any two lines.
c. Name all the points on plane P.
d. Name three collinear points
e. Name the plane that contains point A
f.. Decide whether the following statement is true or false.
“Points F, D, and B are coplanar.”
9
10
EXERCISE XIII: Use the figures to name the following.
1. Three collinear points ____________
2. Four coplanar points ____________
3. A plane containing E ____________
4. Two points and a line that lie in plane T ____________
5. Two planes that contain l ____________
6. The intersection of line TV and line US ____________
7. The intersection of
and plane
8. The intersection of TU and UV ____________
10
11
EXERCISE XIV: Refer to the diagram:
a) Name 2 planes that intersect in line HG . ____________
b) Are the points A, B, C and D collinear? ____________
c) Are the points A, B, C and D coplanar? ____________
d) Name 2 planes that do not intersect. ___________
e) Name 3 lines that intersect at C. ____________
EXERCISE XV: Complete with always, sometimes, or never.
1) Three points ______________ determine a plane.
2) Two points ______________ lie in exactly one line.
3) Three points ______________ lie in exactly one line.
4) Three collinear points ______________ lie in exactly one plane.
5) Two planes ______________ intersect.
6) Two intersecting planes ______________ intersect in exactly one point.
7) Two intersecting lines ______________ intersect in exactly one point.
8) Two lines ______________ intersect in exactly one point.
9) Two intersecting lines ______________ lie in exactly one plane.
10) A line and a point not on that line ______________ lie in more than one plane.
11) A line ______________ contains exactly one point.
12) When A and B are in a plane, 
is ______________ in that plane.
AB
11
12
SELECTIVE RESPONSE
1. Identify an example of an undefined term:
A. a point
B. collinear points
C. non-collinear points D. coplanar points
E. non-coplanar points
2. All of the following are correct names for the line except:
3. The ceiling of our classroom is an example of a:
A. point
B. line
C. plane
D. defined term
E. none of the above
4. The meeting place of two geometric objects is called:
A. a point
B. a line
C. a plane
D. collinear
E. an intersection
5. How many non-coplanar points define space?
6. How many non-coplanar points define space?A. 1
7. How many points define a line?A. 1
B. 2
8. How many non-collinear points define a plane? A. 1
B. 2
C. 3
B. 2
C. 3
D. 4
C. 3
D. 4
E. 5
E. 5
D. 4
E. 5
9. The intersection of two planes is a:
A. point
B. segment
C. line
D. ray
10. The intersection of a line and a plane is a: A. point
B. segment
E. plane
C. line
D. ray
E. plane
11. All of the following statements are true except
A. Two intersecting lines meet at a point.
C. Adjacent angles share a side and a vertex.
B. Opposite rays share an endpoint.
D. Co-planar points are points on the same plane.
E. Obtuse angles measure less than 90 degrees.
12)All of the following statements are true except:
B. The intersection of two planes is a point.
A. Opposite rays share an endpoint.
C. Four non-coplanar points determine space.
D.
Obtuse angles measure more than 90 degrees. E. Congruent segments have the same length.
12
13
13) Which of the following best describes a counterexample to the assertion below:
Two lines in a plane always intersect in exactly one point.
A. coplanar lines
B. parallel lines C. perpendicular lines D. intersecting lines E. none of the
above
14) Which of the following is an example of an undefined term?
A. a ray
B. an angle bisector
C. a midpoint of a segment D. a line
E. vertical angles
15)All of the following statements are true except:
A. Two intersecting lines meet at a point.
B. Opposite rays share an
endpoint.
C. Adjacent angles share a side and a vertex.
D. Co-planar points are points on the same plane. E. Obtuse angles measure less than 90
degrees.
16: In general, a plane is represented by a ______.
A) rectangle or parallelogram
B) lines
C) points
D) sphere
17: The line drawn through two different points in a plane _______ lies in the plane containing the
two points. A) sometimes completely, sometimes partially
B) always partially
C) always
completely
18: The relationships between points and lines in a plane are called _____.
A) linear properties
B) planar properties
C) surface properties
D) incidence
properties
19: The number of surfaces that a cylinder contains is _____.
A) three
B) two
C) one
20: The symbol '||' represents
A) perpendicular lines
B) intersecting lines
C) parallel lines
D) finite
lines
21: Two intersecting lines in a plane have ________ common point(s). A) only three B) only one C)
only two C) many
22: _____ line (or lines) can be drawn through two different points in a plane.
A) Many
B) Only one
C) Two
D) Only three
23: Two different lines in a plane having a common point are called _____.
A) intersecting lines
B) common lines
C) parallel lines
D) point lines
13
14
14