GEOMETRY
Legal Reasons
Level 2
Convex sets,
Counterexamples, Midpoints, Circles, Union, Intersection, Triangles
|
1
|
Definition of Convex Set
|
A convex set is a set in which every segment that connects points
of the set lies entirely in the set.
|
2
|
Definition
of Instance |
An
instance of a conditional is a specific case in which both the antecedent
(if part) and the consequent (then part) of the conditional
are true. |
3
|
Definition of Counterexample
|
A counterexample to a statement is a specific case for which
the antecedent, if part, is true but the consequent, then
part, is false.
If even one counterexample can be found for a given statement,
then the statement is not true.
Example: Consider the statement, "For all x's, x^2 >x." This
is not a true statement because if x =1, then
x^2 =1 also, and one is NOT greater than itself.
|
4 |
Definition
of Converse |
If you want to write
the converse of a conditional, switch the antecedent, (if part),
with the consequent, (then part).
|
5
|
Definition of Midpoint
|
The midpoint of
is the point M on
with AM = MB.
|
6
|
Definition of Circle
|
A circle is the set of all points in a plane at
a certain distance, its radius, from a certain point, its center.
|
7
|
Definition
of radius of a circle |
The
radius of a circle is the distance from the center of the circle
to any point on the circle. |
8
|
Definition
of Diameter of a circle |
The
diameter of a circle is equal to two times the radius. (d = 2r) |
9
|
Definition of Union
|
The union of two sets A and B, written A U B, is the set of elements
which are in A, in B, or in both A and B.
|
10
|
Definition of Intersection
|
The intersection of two sets A and B written ,
is the set of elements which are in both A and B.
|
11
|
Definition
of Complement |
The complement of set
A, written ~A, is all the elements which are not in set
A.
Ex: set B intersected with everything not in set A would look
like this,
.
|
12 |
Definition of Polygon
|
A polygon is the union of segments in the same plane such that
each segment intersects exactly two others, one at each of its
endpoints.
|
13 |
Definition of Equilateral Triangle
|
An equilateral triangle is one with all three sides equal in
length.
|
14 |
Definition of Isosceles Triangle
|
An isosceles triangle is one with AT LEAST two sides of equal
length.
|
15 |
Definition of Scalene Triangle
|
A scalene triangle has no sides equal in length.
|
16 |
Triangle Inequality Postulate
|
The sum of the lengths of any two sides of a triangle is greater
than the length of the third side.
Example: 3in, 4in, and 10in cannot be the sides of a triangle
because 3 + 4 is not greater than 10.
The two short sides are not long enough to meet up and close the
triangle.
|