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Geometry Quiz 1

UCSMR Geometry 1-6, 1-7, 1-8 Quiz Stack

Circularity One word the defines another and then that word defines the first.
undefined terms words that have no definition
figure a set of points
space a set of all points
collinear 3 or more points are collinear iff they lie on the same line
coplanar 4 or more points are coplanar iff they lie on the same plane
one-dimensional length (ft, m, etc)
two-dimensional length and width (area) (ft^2 or m^2)
three-dimensional length, width, and height (volume) (ft^3 or m^3)
Euclidean Geometry parallel lines NEVER touch/study of Euclid's works (Greek Mathematician)
Spherical Geometry parallel lines do meet
Iff if and only if, bi-conditional statement
plane any flat surface that repeats in ALL directions (parallelogram describes this)
Postulates statements assumed to be true
Point-Line-Place Postulate a.)Unique Line Assumption - through any two points there is exactly one line.
b.)Number Line Assumption - any line can be turned into a number line.
c.)Dimensional Assumption - (1) Given a line in a plane there is at least one point in the plane and not on the line. (2)Given a plane in space, there is at least one point in space, not on the plane.
theorem statements which are proven true
Line Intersect Theorem Two Lines intersect in at most one point, (on the same plane).
parallel lines two coplanar are parallel lines iff they have no points in common or they're identitcal.
m//n lines m and n are parallel
Betweenness of Numbers a number is between two other points if it is greater than one and less than the other.
Betweenness of Points a point is between two other points if it is on the same line and its coordinate is between their coordinates.
segment(line segment) with endpoint A and B, is the set consisting of the distinct points A and B and all points between A and B.
ray with endpoint A and containing a second point B, consists of the points on AB(ray) and all points for which B is between each of them and A. Rules: (ray)AB is not the same as (ray)BA, they would travel in opposite directions therefore the order matters!
Distance Postulate a.) Uniqueness Property - on a line, there is a unique distance between two points, (only one correct answer).
b.) Distance Formula - if two points on a line have coordinates x and y then the distance between them is (x-y).
c.) Additive Property - if b is on (segment) AC, then AB+BC=AC
Created by: nigel.flynn