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Understanding Points, Lines, and Planes in Geometry

Learn about the basic properties of geometry and how they relate to the real world. Explore points, lines, and planes, as well as coplanar and collinear points. Practice postulates and intersection concepts.

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Understanding Points, Lines, and Planes in Geometry

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  1. Warm-Up 2/1/13 Describe any points, lines and planes you see in this picture

  2. Unit 2: Introduction to Geometry • Essential Question: • How do the basic properties of geometry apply to the real world? How do you use deductive reasoning, logic, and mathematical properties to help you draw conclusions? • Bonus Question: • Write real-world examples of conditionals and converses that meet the following criteria, and explain each answer. • A) Write a conditional that is true but whose converse is false. • B) Write a true conditional whose converse is also true.

  3. Point Points, Lines, and Planes Definition: A point is an indication of a location. A point has no size. A point is represented by a small dot and is named by a capital letter Example: Name: Point A A

  4. Line Definition: A line is a series of points that extends in two opposite directions without end. You can name a line by any two points on the line. Another way to name a line is with a single lowercase letter. Names: **must be only two points**

  5. Collinear points Definition: Collinear points are points that lie on the same line. In the picture below, points A and B are collinear but C is not Name the collinear points: B A C

  6. Plane Definition: A plane is a flat surface that has no thickness. A plane contains many lines and extends without end in the directions of all its lines. You can name a plane by either a single capital letter or by at least three of its non-collinear points. Vertical • Horizontal Plane Plane A C B P

  7. Plane • Names:

  8. Coplanar Definition: Points and lines in the same plane are coplanar. M P

  9. Naming a Plane

  10. Space: Space is the boundless, three-dimensional set of all points

  11. Intersection Intersection: the set of points that two figures have in common.

  12. Basic Postulates of Geometry (A Postulate is a rule accepted as true without proof) Draw two points and connect the points. What is the geometric figure.

  13. Postulate 1-1 • Through any two points there is exactly one line. • Line t is the only line that passes through points A and B. t B A

  14. Postulate 1-2 • If two lines intersect, then they intersect in exactly one point • AE and BD intersect at C A B C D E

  15. What is the intersection of the front wall and the ceiling?

  16. Postulate 1-3 • If two planes intersect, then they intersect in exactly one line. • Plane RST and plane STW intersect in ST R T S W

  17. Postulate 1-4 • Through any three noncollinear points there is exactly one plane

  18. a) Name the plane on the bottom of the box • b) Shade the plane that contains E, H, and C. • c) Name another point that is in the same plane of point A, B, and C. • d) Name another point that is coplanar with points E, H, and C. • e) Are points A and G collinear?

  19. 2. Name the intersection of… A. Planes HGF and GCB GF B. Planes HDC and DAB DC C. Planes EHD and FGC None

  20. d. Plane EFB and Point B e. Plane HEB and Point C f. Plane HEF and Point F

  21. Homework • Practice 1-2 • Quiz Wednesday!

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