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Understanding Geometry: Points, Lines, and Planes

This introduction to geometry explores the fundamental concepts including points, lines, and planes, which serve as the building blocks of the subject. Learn about key definitions, such as the characteristics of points (location without size), lines (infinite length with no thickness), and planes (flat surfaces extending infinitely). The postulates that govern their relationships are also discussed. Understanding these concepts is essential for further study in geometry and related fields, making it a vital foundation for students and enthusiasts alike.

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Understanding Geometry: Points, Lines, and Planes

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  1. 1-2Points, Lines and Planes

  2. What is geometry? What did the acorn say after it grew up? Gee, I’m a tree Geo:metry: Definition: A statement that explains the meaning of a word or phrase Format for notes: (Optional method) Earth Measure

  3. Building BlocksUndefined terms • Point • Most basic building block of geometry • It has no size, only location • Notation: Capital Letter • Line • A straight, continuous arrangement of infinitely many points • Infinite length but no thickness • Extends forever in two directions • Notation: Naming any two points on line with line symbol above • Plane • Length and width but no thickness. • Like a flat surface that extends infinitely along its length and width. • Notation: Script Capital Letter P B A P

  4. More Terms F E P R • Collinear • On the same line • Coplanar • On the same plane • Line Segment (segment) • Two points called endpoints of the segment and all the points between them that are collinear with the two points. • Notation: • Length: D Q B 5 cm A Endpoints

  5. B More Terms A D • Congruent Segments • Two segments with the same lengths • Symbol: • Notation: • Marking figures • Midpoint • A point that divides the segment into two congruent segments C Midpoint O N M

  6. …aaaaand more… • Ray • A part of a line that begins at a point and extends infinitely in one direction. • Notation: A D • Opposite Rays • Two rays that share the same endpoint and form a line. • Notation: A C and B

  7. Examples 5. Name congruent segments 1. Name a line 3. Name a ray 2. Name a line segment 4. Name a midpoint K A D L B F M C N

  8. A postulate or axiom is an accepted statement of fact. Postulate 1-1 Through any two points there is exactly one line. Line t passes through points A and B. Line t is the only line that passes through both points. B p. 16: 9-49 odd, 53-59 A Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one point. t A B C and intersect at point C. E D

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