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

2. Describe Geometric Figures
Target
Describe Geometric Figures
You will …
Identify points, lines, and planes. Name and sketch geometric figures.

3. Vocabulary
Three undefined terms of geometry –
point – has no dimension; represented by a dot
line – has one dimension; represented by a line with arrows; extends without end Postulate 5
plane – has two dimensions; represented by a parallelogram; extends without end Postulate 8

4. Vocabulary
Defined terms of geometry – terms that can be described with known words such as point, line and plane
Line AB ( or AB ) is used here to define these terms.
line segment AB ( AB ) – consists of endpoints A and B and all points on AB that lie between A and B
ray AB ( AB ) – consists of endpoint A and all points on AB that lie on the same side of A as B

5. Vocabulary
Collinear
Points are collinear if they lie on the same line.
Segments and rays are collinear if they lie on the same line.
If points A, B, and C are collinear and C is between A and B, then CA and CB are opposite rays.
Coplanar
Points are coplanar if they lie in the same plane.
Lines, segments and rays are coplanar if they lie in the same plane.

6. EXAMPLE 1
Name points, lines, and planes
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.

7. EXAMPLE 1
Name points, lines, and planes
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.

8. 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

9. EXAMPLE 2
Name segments, rays, and opposite rays
a. Give another name for GH .
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 .

10. GUIDED PRACTICE
for Example 2
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.

11. 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.

12. 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

13. GUIDED PRACTICE
for Examples 3 and 4
Sketch two different lines that intersect a plane at the same point.
ANSWER

14. GUIDED PRACTICE
for Examples 3 and 4
Use the diagram at the right.
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