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Geometry

Geometry. Lesson 1 – 1 Points, Lines, and Planes. Objective: Identify and model points, lines, and planes. Identify intersecting lines and planes. Undefined terms. Undefined terms : objects that are only explained using examples and descriptions. Point Line Plane. Point. Point:

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Geometry

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  1. Geometry Lesson 1 – 1 Points, Lines, and Planes Objective: Identify and model points, lines, and planes. Identify intersecting lines and planes.

  2. Undefined terms • Undefined terms: objects that are only explained using examples and descriptions. • Point • Line • Plane

  3. Point • Point: • A point is a location. • Has neither shape nor size • Named: • Capital letter • Example • Point A

  4. Line • Line: • Made up of points • Has no thickness or width • Exactly one line through and two points. • Named: • Any 2 points on the line (2 capital letters) • Lowercase script letter • Example • line m or

  5. Plane • Plane: • A flat surface made up of points that extends infinitely in all directions. • Exactly one plane through any 3 points not on the same line. • Named • Capital Script letter • 3 points on the plane not on a line (3 capital letters) • Example K Plane BCD (any order)

  6. Definitions • Collinear: • Points that lie on the same line • Noncollinear: • Points that do not lie on the same line. • Coplanar • Points that lie in the same plane • Noncoplanar • Points that do not line in the same plane

  7. Use the figure to name each of the following: • A line containing point W • A plane containing point X Any one of the following work: Any one of the following work: (3 letters that are noncollinear) P, plane XZY, plane VZY, plane VZW, plane WZX, plane VZX, Plane WZY

  8. Example • Name the geometric term modeled by the objects in the picture. • Push pin • Maroon boarder • The card itself • Stripes on a sweater • Corner of a box Point G Sample: plane FGJ lines point

  9. Intersection At a point. • Intersection of two or more geometric figures is the set of points they have in common. • Where do two lines intersect? • Where do two planes intersect? At a line

  10. Draw the following • intersects plane T at point S. Sample answer Must have the dashed line to show that the line goes through the plane and is not on or in the plane.

  11. Draw the following • Line p lies in plane N and contains point L. Sample answer.

  12. Definitions • Definitions are defined terms that are explained using undefined terms and/or other defined terms. • Space: defined as a boundless, three-dimensional set of all points. Space can contain lines and planes.

  13. 6 planes: 5 around the pyramid and one on bottom of the the pyramid… don’t name the bottom plane twice. • How many planes appear in this figure. • Name 3 points that are collinear. • Name the intersection of plane HDG with plane X. • At what point do LM and EF intersect? Explain. Points J, K, and D Make sure you have commas otherwise it names a plane. Don’t appear to intersect since L is the only point on line LM in the plane.

  14. No, not all on the same plane. • Are points E, D, F, and G coplanar? • At what point or in what line do planes JDH, JDE, and EDF intersect? Point D is the only thing in common.

  15. Homework • Pg. 8 1 – 12 all, 14 – 46 EOE, 52, 66 – 82 EOE

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