Chapter 2 Flashcards
(45 cards)
What is the union of a half line and it’s origin, and it extends infinitely in one direction from a point.
It’s a ray.
What is the set off all points on a line on a given side of a given point of the line
A half-line
What postulate is that every point divides any line through that point into three disjoint sets, the point and to half lines.
Postulate 2.1 the line separation postulate
When a line contains at least two points and a plane contains at least four noncoplanar points. And a space contains at least 3 noncolinear points.
Postulate 1.1 the expansion postulate.
Any two points in space lie in exactly one line.
Postulate 1.2 the line postulate
When there are three distinct noncolinear points in exactly one plane.
The plane postulate postulate 1.3
If two points lie in one plane the that line contains these two points in exactly one plane.
Postulate 1.4 the flat line postulate
When when two planes intersect they only intersect in one line.
Postulate 1.5 the plane intersection postulate
What postulate is that every line divides any plane containing the line into three disjoint sets: the line and two half-planes.
Postulate 2.2
What is the Jordan Curve Theorem?
It is any simple closed curve divides a plane into three disjoint sets: the curve itself, it’s interior, and its exterior.
What is a half-plane?
It’s a subset of a plane consisting of all points on a given side of a line in the plane. If points P and Q are in the same half-plane then so is the segment joining them.
What is a closed simple and a closed simple curve?
A closed curve is a curve that begins were it ends.
A simple curve that doesn’t intersect with it self at all.
A closed and simple curve is a simple and closed curve.
What is a radius a diameter a chord of a circle an arc and a circle?
An arc is a curve that is a subset of a circle.
A diameter is a chord that passes through the center of the circle.
A radius is half of a diameter.
A center of a circle is the given point in the plane.
A circle is a set of all points that are given distance from a given point in a given plane.
What is the interior and exterior of a circle?
The exterior of a circle is the set of all planar points whose distance from the center is greater than the length of the radius.
The interior of a circle is the set of all planar points whose distance from the center is less than the length of the radius.
What is a region?
The union of a simple closed curve and its interior, and the curve is the boundary of the region.
What is a convex?
The set that has the property that any two of its points determine a segment contained in the set.
What is concave?
A set that is not convex.
What is a polygon?
A simple closed curve that consists only of segment
What is the side of a polygon?
One of the segments that define the polygon.
What is the vertex of a polygon?
An endpoint of a side of a polygon.
What is the side of a polygon?
An angle with two properties: it’s vertex is a vertex of the polygon and each side of the polygon.
What is the vertex of an angle?
The endpoint of two rays.
What are the sides of an angle ?
Two rays that for. an angle.
What is an angle?
Two distinct rays with a common endpoint.
