This document defines key geometry concepts such as points, lines, planes, and their relationships. It provides examples of naming points, lines, and planes, including collinear points that lie on the same line and coplanar points that lie in the same plane. Examples also demonstrate naming segments and rays with different endpoints, and identifying opposite rays. Diagrams show intersecting lines and planes, including lines within a plane, lines that do not intersect a plane, and lines intersecting a plane at a point. Two intersecting planes are shown meeting at a line of intersection. Guided practice problems apply the concepts to name intersections and identify relationships in diagrams.

1. 1.1 Key Concepts1.1 Key Concepts

2. Undefined TermsUndefined Terms
Words that do not have formalWords that do not have formal
definitions but there is andefinitions but there is an
agreement about what theyagreement about what they
mean.mean.

3. PointPoint

4. LineLine

5. PlanePlane

6. Collinear PointsCollinear Points

7. Coplanar PointsCoplanar Points

8. Defined TermsDefined Terms
Terms that can be describedTerms that can be described
using known terms like Point orusing known terms like Point or
LineLine

9. SegmentSegment

10. RayRay

11. Opposite RayOpposite Ray

12. IntersectionIntersection

13. SOLUTION
EXAMPLE 1 Name points, lines, and planes
b. Name three points that are collinear.
Name four points that are coplanar.
a. Other names for PQ are QP and line n.
Other names for plane R are plane SVT
and plane PTV.
a. Give two other names for PQ and for plane R.

14. EXAMPLE 1 Name points, lines, and planes
b. 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.

15. GUIDED PRACTICE for Example 1
ANSWER TS, PT; point V
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.

16. EXAMPLE 2 Name segments, rays, and opposite rays
b. Name all rays with endpoint J .
Which of these rays are opposite rays?
SOLUTION
a. Another name for GH is HG .
b. The rays with endpoint J are JE , JG , JF , and JH .
The pairs of opposite rays with endpoint J
are JE and JF , and JG and JH .
a. Give another name for GH .

17. GUIDED PRACTICE for Example 2
3. Are HJ and JH the same ray ? Are HJ and HG the
same ray? Explain.
ANSWER FE
ANSWER
No; the rays have different endpoints.
Yes; points J and G lie on the same side of H.
2. Give another name for EF

18. 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.

19. EXAMPLE 4 Sketch intersections of planes
Sketch two planes that intersect in a line.
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
Draw: a vertical plane.
Shade the plane.
STEP 1

20. GUIDED PRACTICE for Examples 3 and 4
4. Sketch two different lines that intersect a plane
at the same point.
Use the diagram at the right.
5. Name the intersection of PQ and line k.
ANSWER Point M
ANSWER

21. GUIDED PRACTICE for Examples 3 and 4
6. Name the intersection of plane A and plane B.
7. Name the intersection of line k and plane A.
ANSWER Line k
ANSWER Line k
Use the diagram at the right.