Background Historically, much of geometry was developed as
Euclidean geometry, or non-coordinate geometry. It was named after
the Greek mathematician Euclid. Euclids most important work was the
13 volumes of The Elements of Geometry. He began his system of
geometry with three undefined terms: point, line, and plane. From
those terms he defined other geometric vocabulary and postulates.
Euclid then proceeded to prove theorems using the definitions and
postulates, much as we do today.
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Geometric Vocabulary Undefined Terms: These terms can only be
explained using examples and descriptions. These undefined terms
can be used to define other geometric terms and properties. (The
building blocks of geometry.) Point Line Plane
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Point Description: Has no actual size, used to represent an
abject or location in space. Naming: Named by a capital letter.
Symbolic Representation:
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Line Description: Has no thickness or width, used to represent
a continuous set of linear points that extend indefinitely in both
directions. Naming: Named by a lowercase script letter or by two
points on the line. Symbolic Representation:
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Plane Description: Has no thickness, width, or depth, used to
represent a flat surface that extends indefinitely in all
directions. Naming: Named by a capital script letter or by three
non-collinear points in the plane. Symbolic Representation:
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Defined Terms All other terms in geometry must be definable and
a definition included a category and then a list of critical
attributes. Example: Space - Set of all points, boundless and
three-dimensional. Set of all points is the classification
Boundless and three dimensional are the critical attributes that
make this definition different from other definitions
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Defined Terms Space Set of all points, boundless and three
dimensional.
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Defined Terms Collinear Set of points, that all lie in the same
line. Two points are always collinear. Three points must be checked
to determine if they are collinear.
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Defined Terms Non-collinear Set of points, that do not all lie
on the same line.
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Defined Terms Coplanar Set of points, or lines, that lie in the
same plane. Three points are always coplanar. Four points must be
checked to determine if they are coplanar.
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Defined Terms Non-Coplanar Set of points, or lines, that do not
lie in the same plane.
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Defined Terms Skew Lines Two non-coplanar lines that do not
intersect.
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Defined Terms Parallel Lines Two coplanar lines that do not
intersect (same slope in y = mx +b form).
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Defined Terms Perpendicular Lines Two coplanar lines that
intersect at right angles (opposite reciprocal slopes in y = mx + b
form).
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Intersections of geometric terms Two lines intersect at a
point
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Intersections of geometric terms Two planes intersect at a
line
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Intersections of geometric terms A line and a plane intersect
at a point
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Unit 1: Foundations of Geometry
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Guided Practice
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Unit 1: Foundations of Geometry
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Definitions
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Examples
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Ruler Postulate Points on a line can be paired with real
numbers and the distance between the two points can be found by
finding the absolute value of the difference between the numbers.
Remember, all distance measures must be
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Examples
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Ruler Postulate The Ruler Postulate can also be used to find
the coordinate of a segments endpoint given the other endpoint and
the segments length.
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Examples:
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Definitions
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Guided Practice
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Constructions
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Examples
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Unit 1: Foundations of Geometry
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Definitions:
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Angles can be named by the vertex point if there are no other
angles that could be confused. three letters with the vertex as the
center and the other letters representing points from each side. a
small number if one is given in the angle.
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Examples:
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Classifying Angles:
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Examples:
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Protractor Postulate:
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Example:
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Angle Addition Postulate:
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Examples:
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Angle Relationships:
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Examples:
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Angle Constructions
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Examples
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Unit 1: Foundations of Geometry
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True/False Summary
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Examples
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And Statement
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Or Statement
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Logic Statement Summary
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And Truth Table
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Or Truth Table
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Unit 1: Foundations of Geometry
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Use the following conditional statement in determining your
responses: If I get paid today, then I will take you to the
movies.
