1. Understanding Points, 1-1 Lines, and Planes Warm Up
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry

2. Objectives
Identify, name, and draw points, lines, segments, rays, and planes.
Apply basic facts about points, lines, and planes.

3. Vocabulary
undefined term point
line plane
collinear coplanar
segment endpoint
ray opposite rays
postulate

4. 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.

9. Points that lie on the same line are collinear
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. M K L N

10. 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

11. Name points, lines, and planes
EXAMPLE 1
Name points, lines, and planes
Give two other names for PQ and for plane R.
b. 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.

12. Name points, lines, and planes
EXAMPLE 1
Name points, lines, and planes
Points S, P, and T lie on the same line, so they are collinear.
Points S, P, T,and V lie in the same plane, so they are coplanar.

13. GUIDED PRACTICE
for Example 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
TS, PT; point V

14. Example 2: Drawing Segments and Rays
Draw and label each of the following.
A. a segment with endpoints M and N. M N
B. opposite rays with a common endpoint T. T

15. Check It Out! Example 2
Draw and label a ray with endpoint M that contains N. M N

16. Check It Out! Example 3
Name a plane that contains three noncollinear points.
Possible answer: plane GHF

17. 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.

18. 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.

19. Sketch intersections of lines and planes
EXAMPLE 3
Sketch intersections of lines and planes
a. 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 a. b. c.

20. Sketch intersections of planes
EXAMPLE 4
Sketch intersections of planes
Sketch two planes that intersect in a line.
Draw: a vertical plane. Shade the plane.
STEP 1
SOLUTION
Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden.
STEP 2
Draw: the line of intersection.
STEP 3

21. Sketch two different lines that intersect a plane at the same point.
GUIDED PRACTICE
for Examples 3 and 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
Point M

22. 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

23. 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