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Building Blocks Of Geometry
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    Building Blocks Of Geometry Building Blocks Of Geometry Presentation Transcript

    • Building Blocks of Geometry
    • The Building Blocks
      • Point
      • Plane
      • Line
      • These 3 objects are used to make all of the other objects that we will use in Geometry
      • What do you think it means to be a “Building block of Geometry? What might one be?
    • Point
      • The most basic building block
      • Has no size
      • Only has a Location
      • Representation
        • Shown by a Dot
        • Named with a single Capital letter
      • Ex:
      • What would a real world example be? = “Point P”
    • Line
      • A straight, arrangement of infinitely many points.
      • Infinite length, but no thickness
      • Extends forever in 2 directions
      • Named by any 2 points on the line with the line symbol above the letters (order does not matter
      • Ex:
      = “Line AB” or “Line BA”
      • Real World Example?
    • Plane
      • An imaginary flat surface that is infinitely large and with zero thickness
      • Has length and width, but no thickness
      • It is like a flat surface that extends infinitely along its length and width
      • Represented by a 4 sided figure, like a tilted piece of paper
        • This is really only part of a plane
      • Named with a Capital Cursive letter
      • Ex:
      = “Plane P”
      • Real World Example?
    • Explaining the Objects
      • Can be difficult
      • Early Mathematicians attempted to:
      • Ancient Greeks
        • “ A point is that which has no part. A line is a breathless length.”
      • Ancient Chinese Philosophers
        • “ The line is divided into parts, and that part which has no remaining part is a point.”
    • What’s the Problem?
    • Definitions
      • A definition is a statement that clarifies or explains the meaning of a word or phrase
      • It is impossible to define “point,” “line,” and “plane” without using words or phrases that need to be defined.
        • Therefore we refer to these building blocks as “Undefined”
      • Despite being undefined, these objects are the basis for all geometry
        • Using the terms “point,” “line,” and “plane,” we can define all other geometry terms and geometric figures
    • Definitions
      • Collinear – Lie on the same line
        • Example – Points A and B are “Collinear”
    • Definitions
      • Coplanar – Lie on the same plane
        • Example – Point A, Point B, and Line CD are “Coplanar.”
    • Definitions
      • Line Segment – Two points (called endpoints) and all of the points between them that are collinear.
        • In other words, a portion of a line
        • Represent a Line Segment by writing its endpoints with a bar over the top
        • Example:
    • Definitions
      • Ray – Begins at a single point and extends infinitely in one direction
        • Example:
        • You need 2 points to name a ray, the first is the endpoint , and the second is any other point that the ray passes through .
    • Definitions
      • Congruent – equal in size and shape
        • We mark 2 congruent segments by placing the same number of slash marks on them.
        • The symbol for congruence is and you say it as “is congruent to.”
        • Example:
    • Definitions
      • Bisect – Divide into 2 congruent parts
      • Midpoint – the point on the segment that is the same distance from both endpoints.
        • The midpoint bisects the segment
    • Definitions
      • Parallel Lines – 2 lines that never intersect
        • We mark 2 lines as parallel by placing the same number of arrow marks on them.
        • Example:
        • To write this as a statement, we would write
    • Definitions
      • Perpendicular Lines – 2 lines that intersect at a Right Angle (90°).
        • We mark 2 lines as Perpendicular by placing a small square in the corner where they cross
        • Example:
        • To write this as a statement, we would write:
      • Things you may Assume
        • You may assume that lines are straight, and if 2 lines intersect, they intersect at 1 point.
        • 2) You may assume that points on a line are collinear and that all points & objects shown in a diagram are coplanar unless planes are drawn to show that they are not coplanar.
      • Things you may NOT Assume
        • You may not assume that just because 2 lines, segments, or rays look parallel that they are parallel – they must be marked parallel
        • You may not assume that 2 lines are perpendicular just because they look perpendicular – they must be marked perpendicular
        • Pairs of angles, segments, or polygons are not necessarily congruent, unless they are marked with information that tells you that they are congruent.