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1. Understanding Points, Lines, and Planes 1-1 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.

6. K L M N 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.

7. Possible answer: AE, BE, CE Example 1: Naming Points, Lines, and Planes A. Name four coplanar points. A, B, C, D B. Name three lines.

8. Check It Out! Example 1 Use the diagram to name two planes. Possible answer: PlaneRand plane ABC.

9. a. Give two other names for PQand for plane R. b.Name three points that are collinear. Name four points that are coplanar. Other names for PQare QPand line n. Other names for plane Rare plane SVT and plane PTV. EXAMPLE 1 Name points, lines, and planes SOLUTION

10. EXAMPLE 1 Name points, lines, and planes • Points S, P, and Tlie on the same line, so they are collinear. • Points S, P, T,andVlie in the same plane, so they are coplanar.

11. 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 for Example 1 GUIDED PRACTICE

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

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

16. XY Example 3: Identifying Points and Lines in a Plane Name a line that passes through two points.

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

19. Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen.

20. 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.

21. 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.

22. c. a. b. 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

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

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

25. CB and CD 2. A point on BC. Possible answer: BD Lesson Quiz: Part I 1. Two opposite rays. Possible answer: D 3. The intersection of plane N and plane T. 4. A plane containing E, D, and B. Plane T

26. 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