Understanding
Points,
Understanding
Points,
Lines, and Planes
1-1
1-1
Lines, and Planes
Warm Up
Lesson Presentation
Lesson Quiz
Holt
HoltGeometry
McDougal
McDougalGeometry
Geometry
1-1 Understanding Points, Lines, and Planes
Objectives
Identify, name, and draw points, lines,
segments, rays, and planes.
Apply basic facts about points, lines,
and planes.
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Vocabulary
undefined term
line
collinear
segment
ray
postulate
Holt McDougal Geometry
point
plane
coplanar
endpoint
opposite rays
1-1 Understanding Points, Lines, and Planes
The most basic figures in
geometry are undefined terms,
which cannot be defined by using
other figures. The undefined
terms point, line, and plane are
the building blocks of geometry.
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Points that lie on the same line are collinear.
K, L, and M are collinear. K, L, and N are
noncollinear. Points that lie on the same
plane are coplanar. Otherwise they are
noncoplanar.
K
L M
N
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Example 1: Naming Points, Lines, and Planes
A. Name four coplanar points.
A, B, C, D
B. Name three lines.
Possible answer: AE, BE, CE
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Check It Out! Example 1
Use the diagram to name two planes.
Possible answer:
Plane R and plane ABC.
Holt McDougal Geometry
.
Understanding Points, Lines, and Planes
1-1
EXAMPLE
Name points,
1
lines, and planes
a. Give two other names for PQ and for
plane R.
Name three points that are collinear.
Name four points that are coplanar.
SOLUTION
Other names for PQ are QP and line n.
Other names for plane R are plane SVT
and plane PTV.
Holt McDougal Geometry
Understanding Points, Lines, and Planes
1-1
EXAMPLE
Name points,
1
lines, and planes
b. Points S, P, and T lie on the same
line, so they are collinear.
c. Points S, P, T,and V lie in the same
plane, so they are coplanar.
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
GUIDED PRACTICE for Example 1
1.
Use the diagram in Example 1. Give
two other names for ST . Name a
point that is not coplanar with points
Q, S, and T.
ANSWER
Holt McDougal Geometry
TS, PT; point V
1-1 Understanding Points, Lines, and Planes
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Example 2: Drawing Segments and Rays
Draw and label each of the following.
A. a segment with endpoints M and N.
N
M
B. opposite rays with a common endpoint T.
T
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Check It Out! Example 2
Draw and label a ray with endpoint M that
contains N.
M
Holt McDougal Geometry
N
1-1 Understanding Points, Lines, and Planes
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Example 3: Identifying Points and Lines in a Plane
Name a line that passes through two points.
XY
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Check It Out! Example 3
Name a plane that contains three noncollinear
points.
Possible answer: plane GHF
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Use a dashed line to show the
hidden parts of any figure that
you are drawing. A dashed line
will indicate the part of the figure
that is not seen.
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Example 4: Representing Intersections
A. Sketch two lines intersecting in exactly one
point.
B. Sketch a figure that shows a line that
lies in a plane.
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Check It Out! Example 4
Sketch a figure that shows two lines intersect
in one point in a plane, but only one of the
lines lies in the plane.
Holt McDougal Geometry
Understanding Points, Lines, and Planes
1-1
EXAMPLE
Sketch
3 intersections of lines and planes
Sketch a plane and a line that is in the plane.
b.
Sketch a plane and a line that does
not intersect the plane.
c. Sketch a plane and a line that
intersects the plane at a point.
SOLUTION
c.
a.
b.
Holt McDougal Geometry
Understanding Points, Lines, and Planes
1-1
EXAMPLE Sketch intersections of planes
4
Sketch
two planes that intersect in a line.
SOLUTION
P 1 Draw: a vertical plane.
Shade the plane.
STEP 2 Draw: a second plane that is
horizontal. Shade this plane
a different color. Use dashed
lines to show where one
plane is hidden.
STEP 3 Draw: the line of intersection.
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
GUIDED PRACTICE for Examples
3 and 4
4. Sketch two different lines that
intersect a plane at the same point.
ANSWER
Use the diagram at the right.
5.
Name the intersection of PQ and line k.
ANSWER
Holt McDougal Geometry
Point M
1-1 Understanding Points, Lines, and Planes
Lesson Quiz: Part I
1. Two opposite rays.
CB and CD
2. A point on BC.
Possible answer: D
3. The intersection of plane N and plane T.
Possible answer: BD
4. A plane containing E, D, and B.
Plane T
Holt McDougal Geometry
1-1 Understanding Points, Lines, and Planes
Lesson Quiz: Part II
Draw each of the following.
5. a line intersecting a plane at one point
6. a ray with endpoint P that passes through Q
Holt McDougal Geometry