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Page 6. NCTM Standards: 3, 6, 8, 9, 10. 1.1 Points, Lines, & Planes. A set of points that extends without end in two opposite directions. A set of points that extends in four directions without end. A location in space, represented by a dot. As a dot. With an arrow at each end.

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Page 6

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  1. Page 6 NCTM Standards: 3, 6, 8, 9, 10

  2. 1.1 Points, Lines, & Planes A set of points that extends without end in two opposite directions A set of points that extends in four directions without end A location in space, represented by a dot As a dot With an arrow at each end As a parallelogram A capital cursive letter or 3 noncollinear * points A capital block letter Two points on the line or a lower-case cursive Has immeasurable length, but no width or thickness Has length & width, but no thickness Has no shape or size Line n, line AB, line BA Point P P Plane T, plane XYZ, plane XZY, Plane YXZ, Plane YZX, etc. * Noncollinear: three or more points not in a straight line

  3. 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 b. Points S, P, and Tlie on the same line, so they are collinear. Points S, P, T,and Vlie in the same plane, so they are coplanar.

  4. 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 Other names for ST are TS and PT. Point V is not coplanar with points Q,S and T for Example 1 GUIDED PRACTICE

  5. 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

  6. 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

  7. 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.

  8. ANSWER LineK ANSWER LineK GUIDED PRACTICE 6. Name the intersection of plane A and plane B. 7. Name the intersection of line kand plane A.

  9. H M J G K L

  10. • • U • R T Q

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

  12. HW - Page 9: 2 – 44 evens

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