Geometry Legal Reasons

GEOMETRY Legal Reasons
Level 2
Convex sets, Counterexamples, Midpoints, Circles, Union, Intersection, Triangles


 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.

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.

 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).


Definition of Midpoint

The midpoint of is the point M on with AM = MB.


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.

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.
Definition of Diameter of a circle The diameter of a circle is equal to two times the radius. (d = 2r)

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.


Definition of Intersection

The intersection of two sets A and B written , is the set of elements which are in both A and B.

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,


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.


Definition of Equilateral Triangle

An equilateral triangle is one with all three sides equal in length.


Definition of Isosceles Triangle

An isosceles triangle is one with AT LEAST two sides of equal length.


 Definition of Scalene Triangle

A scalene triangle has no sides equal in length.


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.

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