NCTM Standards: 3, 6, 8, 9, 10

1.1 Points, Lines, & Planes PointLinePlane Definition Model Drawn Named By: Facts Words/ Symbols As a dotWith an arrow at each end A location in space, represented by a dot A set of points that extends without end in two opposite directions A set of points that extends in four directions without end As a parallelogram A capital block letter Two points on the line or a lower-case cursive A capital cursive letter or 3 noncollinear * points Has no shape or size Has immeasurable length, but no width or thickness Has length & width, but no thickness Point P P Line n, line AB, line BA Plane T, plane XYZ, plane XZY, Plane YXZ, Plane YZX, etc. * Noncollinear: three or more points not in a straight line

SOLUTION EXAMPLE 1 Name points, lines, and planes b. Name three points that are collinear. Name four points that are coplanar. a.Other names for PQ are QP and line n. Other names for plane R are plane SVT and plane PTV. a. Give two other names for PQ and for plane R. 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 for Example 1 ANSWER Other names for ST are TS and PT. Point V is not coplanar with points Q, S and T 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.

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.

EXAMPLE 4 Sketch intersections of planes Sketch two planes that intersect in a line. 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 Draw: a vertical plane. Shade the plane. STEP 1

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

GUIDED PRACTICE 6. Name the intersection of plane A and plane B. 7. Name the intersection of line k and plane A. ANSWERLine K ANSWERLine K

G H J K L M

Q T U R

Space A boundless, three-dimensional set of all points. Space can contain lines & planes.

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