Understanding Points, 1-1 Lines, and Planes Warm Up Holt Geometry Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry

Objectives Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.

Vocabulary undefined term point line plane collinear coplanar segment endpoint ray opposite rays postulate

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.

Points that lie on the same line are collinear 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. M K L N

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

Check It Out! Example 1 Use the diagram to name two planes. Possible answer: Plane R and plane ABC.

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

Name points, lines, and planes EXAMPLE 1 Name points, lines, and planes 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 for Example 1 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: Drawing Segments and Rays Draw and label each of the following. A. a segment with endpoints M and N. M N B. opposite rays with a common endpoint T. T

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

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

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

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.

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.

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.

Sketch intersections of lines and planes 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.

Sketch intersections of planes 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

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

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

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