1. Identify Points, Lines, and Planes
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Graph each inequality.
1. x ≤ 1
ANSWER 8
2. –2 ≤ x ≤ 3
ANSWER

3. Warm-Up
3. Juan has more than 5 but fewer than 11 fish in his aquarium. Write an inequality to express the number of fish f Juan has.
ANSWER
5 < f < 11

4. Example 1
Use the diagram.
a. Give two other names for PQ and for plane R.
SOLUTION
Other names for PQ are QP and line n Other names for plane R are plane SVT and plane PTV.

5. Example 1
Use the diagram.
b. Name three points that are collinear.
Name four points that are coplanar.
SOLUTION
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.

6. Guided Practice
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

7. Example 2
Use the diagram.
a. Give another name for GH .
SOLUTION
a. Another name for GH is HG .

8. Example 2
Use the diagram.
b. Name all rays with endpoint J Which of these rays are opposite rays?
SOLUTION
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 .

9. Guided Practice
Use the diagram.
2. Give another name for EF.
ANSWER FE
3. Are HJ and JH the same ray ? Are HJ and HG the same ray? Explain.
ANSWER
No; the rays have different endpoints. Yes; points J and G lie on the same side of H.

10. Example 3
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.

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

12. Guided Practice
Sketch two different lines that intersect a plane at the same point.
ANSWER

13. Guided Practice
Use the diagram at the right.
5. Name the intersection of PQ and line k.
ANSWER
point M
6. Name the intersection of plane A and plane B.
ANSWER
line k
Name the intersection of line k and plane A.
ANSWER
line k

14. Lesson Quiz
Use the figure for exercises 1-4.
1. Give two other names for AE.
EC , AC
ANSWER
2. Give another name for plane S.
ANSWER
Sample answer: plane DEF or EBF

15. Lesson Quiz
Use the figure for exercises 1-4.
3. Name three collinear points.
ANSWER
Sample answer: A, E, C or D, E, B
4. Name the intersection of AC and plane S.
ANSWER E