Page 14 - Standard Handbook Of Petroleum & Natural Gas Engineering

GEOMETRY

See References 1-3 for additional information.
Sets and Functions
A set is a clearly defined collection of distinct objects or elements. The
intersection of two sets S and T is the set of elements which belong to S and
which also belong to T. The union of S and T is the set of all elements which
belong to S or to T (or to both, Le., inclusive or).
A ficnction is a set of ordered elements such that no two ordered pairs have
the same first element, denoted as (x,y) where x is the independent variable
and y is the dependent variable. A function is established when a condition exists
that determines y for each x, the condition usually being defined by an equation
such as y = f(x) [2].

Angles
An angle A may be acute, 0" < A < go", right, A = go", or obtuse, 90" < A < 180".
Directed angles, A 2 0" or 2 180", are discussed in the section "Trigonometry."
Two angles are complementary if their sum is 90" or are supplementary if their
sum is 180". Angles are congruent if they have the same measurement in degrees
and line segments are congruent if they have the same length. A dihedral angle
is formed by two half-planes having the same edge, but not lying in the same plane.
A plane angle is the intersection of a perpendicular plane with a dihedral angle.
Polygons

A polygon is the union of a finite number of triangular regions in a plane,
such that if two regions intersect, their intersection is either a point or a line
segment. Two polygons are similar if corresponding angles are congruent and
corresponding sides are proportional with some constant k of proportionality.
A segment whose end points are two nonconsecutive vertices of a polygon is a
diagonal. The perimeter is the sum of the lengths of the sides.
Triangles

A median of a triangle is a line segment whose end points are a vertex and
the midpoint of the opposite side. An angle bisector of a triangle is a median
that lies on the ray bisecting an angle of the triangle. The altitude of a triangle
is a perpendicular segment from a vertex to the opposite side. The sum of the
angles of a triangle equals 180". An isosceles triangle has two congruent sides
and the angles opposite them are also congruent. If a triangle has three
congruent sides (and, therefore, angles), it is equilateral and equiangular. A scalene

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