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

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

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

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.

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.

Guided Practice 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

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

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 .

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.

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.

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

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

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 7. Name the intersection of line k and plane A. ANSWER line k

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

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