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Geometry Basics and Problem Solving | Building Blocks and Definitions in Geometry

Learn the fundamentals of geometry: points, lines, planes, segments, congruence, and problem-solving skills. Explore ancient definitions, collinear and coplanar points, and develop a strong foundation in geometry. Practical tasks to reinforce learning included.

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Geometry Basics and Problem Solving | Building Blocks and Definitions in Geometry

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  1. Do Now • Take a ruler from the bookshelf. • Have your syllabus contract out and ready to turn in. • Take out your notebook for this class. • In your notebook, describe the two types of symmetry and draw an example of each.

  2. Building Blocks of Geometry

  3. Today’s Objectives • Learn the terminology and notation of points, segments, lines, rays, planes, angles, and collinear and coplanar points. • Learn the idea of congruence of line segments • Learn how to mark congruence of segments on diagrams • Begin keeping a notebook of definitions • Develop Problem Solving Skills

  4. Undefined terms • Point • Line • Plane • The three most basic building blocks of geometry.

  5. Point • Has no size. • Only has location • Represented with a dot • Named by a capital letter

  6. Line • Straight continuous arrangement of infinitely many points. • Has infinite length but no thickness • Extends forever in two directions • Named by the letter names of any two points on the line and the line symbol.

  7. Plane • Has length and width, but no thickness. • Flat surface that extends infinitely along its length and width. • Represented with a 4-sided figure, like paper. • Named with a script capital letter. • P

  8. Ancient “Definitions” • “A point is that which has no part. A line is breadthless length.” –Greeks • “The line is divided into parts, and that part which has no remaining part is a point.” –Chinese

  9. Impossible to define • We would have to use the terms point, line, and plane to define them. • So we accept them as undefined and use them to define everything else in Geometry.

  10. Collinear • On the same line.

  11. Coplanar • On the same plane

  12. Ray • Part of a line • Has an endpoint but extends forever in one direction.

  13. angle • Made up of two rays who share an endpoint.

  14. Line Segment • Consists of two endpoints of the segment and all the points between them that are collinear with the two points.

  15. Congruent • Two segments are congruent if they have equal measures or lengths.

  16. practice

  17. Practice

  18. Practice

  19. Today’s Objectives • Learn the terminology and notation of points, segments, lines, rays, planes, angles, and collinear and coplanar points. • Learn the idea of congruence of line segments • Learn how to mark congruence of segments on diagrams • Begin keeping a notebook of definitions • Develop Problem Solving Skills

  20. Exit slip • Draw and mark a figure in which M is the midpoint of ST, SP=PT and T is the midpoint of PQ. • Explain your reasoning. • Draw an example of collinear points. • Define coplanar.

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