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Section 1.2 Points , Lines and Planes

Section 1.2 Points , Lines and Planes. Objectives/Assignment:. Understand and use the basic undefined terms and defined terms of geometry. Sketch the intersections of lines and planes. Using Undefined terms and definition.

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Section 1.2 Points , Lines and Planes

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  1. Section 1.2 Points, Lines and Planes

  2. Objectives/Assignment: Understand and use the basic undefined terms and defined terms of geometry. Sketch the intersections of lines and planes.

  3. Using Undefined terms and definition A point has no dimension. It is usually represented by a small dot. A point is named by a capital letter. A Point A

  4. Using Undefined terms and definition A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. A line is named by a lower case letter or 2 capital letters with a symbol. p A C B Line p or AB

  5. Using Undefined terms and definition A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end even though the drawing of a plane appears to have edges. You name a plane by using the capital letter or any 3 NON-COLLINEAR points. A M C B D E Plane M or plane ABC

  6. More vocabulary… Collinear points are points that lie on the same line. Coplanar points are points that lie on the same plane.

  7. Ex. 1: Naming Collinear and Coplanar Points Name three points that are collinear Solution: D, E and F lie on the same line, so they are collinear. H G E F D

  8. Ex. 1: Naming Collinear and Coplanar Points Name four points that are coplanar. Solution: D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn. H G E F D

  9. Ex. 2: Naming Collinear and Coplanar Points Name three points that are not collinear. Solution: There are many correct answers. For instance, points H, E, and G do not lie on the same line. H G E F D

  10. More . . . Another undefined concept in geometry is the idea that a point on a line is between two other points on the line. You can use this idea to define other important terms in geometry. Consider the line AB (symbolized by AB). l Line l or AB

  11. More . . . The line segment or segment AB (symbolized by AB) consists of the endpoints A and B, and all points on AB that are between A and B. A B Segment AB l B A Line l or AB

  12. More . . . The ray AB (symbolized by AB) consists of the initial point A and all points on AB that lie on the same side of A as point B. A B Ray AB l B A Line l or AB

  13. More . . . Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions. A B Ray BA l B A Line l or AB

  14. More . . . If C is between A and B, then CA and CB are opposite rays. Opposite rays are rays with the same initial point but extending in opposite directions. l B C A Line l or AB

  15. Ex. 2: Drawing lines, segments and rays Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. K J L Draw J, K and L Then draw JK

  16. Ex. 2: Drawing lines, segments and rays Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. K Draw KL J L

  17. Ex. 2: Drawing lines, segments and rays Draw three noncollinear points J, K, and L. Then draw JK, KL and LJ. K Draw LJ J L

  18. Ex. 3: Drawing Opposite Rays Draw two lines. Label points on the lines and name two pairs of opposite rays. Solution: Points M, N, and X are collinear and X is between M and N. So XM and XN are opposite rays. M Q X P N

  19. Ex. 3: Drawing Opposite Rays Draw two lines. Label points on the lines and name two pairs of opposite rays. Solution: Points P, Q, and X are collinear and X is between P and Q. So XP and XQ are opposite rays. M Q X P N

  20. Ex. 4: Sketching intersections Sketch the figure described. A line that intersects a plane in one point Draw a plane and a line. Emphasize the point where they meet. Dashes indicate where the line is hidden by the plane

  21. Ex. 4: Sketching intersections Sketch the figure described. Two planes that intersect in a line Draw two planes. Emphasize the line where they meet. Dashes indicate where one plane is hidden by the other plane.

  22. Add this assignment to your notes: Practice 1.2 Worksheet You may use your notes, but not your partner!

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