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Larson Geometry Reference – Chapter 1
Definitions
Term/Concept
Description
*Adjacent
Adjacent angles are angles that share a common vertex and a common side but have no points in
common in the interior. Adjacent sides are sides that share a common vertex. B
In simple terms, adjacent means “next to”.
*Angle
The union of two rays having the same end point. The end point is called the vertex of the
angle, and the rays are called the sides of the angle.
An angle with a measure less than 90 degrees
An angle with a measure greater than 90 and less than 180
An angle greater than 180 and less than 360.
An angle with a measure of exactly 90.
An angle with a measure of 180. A straight line.
Two angles that share the same vertex, share a common side and do not overlap.
Two angles whose measures add to 90.
Adjacent angles whose non-common sides are opposite rays.
A pair of angles whose measures add to 180.
Two angles whose sides form two pairs of opposite rays.
A point P is between points A and B if points A, P and B are collinear points, and if
.
A ray, line, or segment that divides an angle into two congruent angles.
Any line, ray, or segment that passes through the midpoint of the segment. A segment bisector
divides a segment into two congruent segments.
Collinear points are points that lie on the same line. Non-collinear points are points that do not
lie on the same line.
Angles are congruent if their measures are equal. Also if angles have equal measures then they
are congruent.
Line segments are congruent if their lengths are equal. Also if line segments have equal lengths
then they are congruent.
Coplanar objects are objects that lie in the same plane. Non-coplanar objects are objects that do
not lie in the same plane.
A polygon in which all interior angles are congruent.
A polygon in which all sides are congruent.
The intersection of two objects is the set of points that are contained in both objects.
A straight object that is infinitely long and infinitely thin. A line has no width and no thickness,
only length. A line may contain an infinite number of points but it must have at least two. A
line is denoted by naming two points on the line with a line over the letters with arrows pointing
AB is adjacent to BAC , AB is adjacent to AC.
Angle, Acute
Angle, Obtuse
Angle, Reflex
Angle, Right
Angle, Straight
Angles, Adjacent
*Angles, Complementary
*Angles, Linear Pair
*Angles, Supplementary
*Angles, Vertical
Betweenness
Bisector, Angle
Bisector, Line Segment
Collinear, Non-Collinear Points
Congruent, Angles
*Congruent, Segments
*Coplanar, Non-Coplanar
Equiangular
*Equilateral
Intersection
Line
*Line Segment
*Midpoint
Opposite Rays
Plane
Point
*Polygon
Polygon, Concave
Polygon, Convex
A
C
in either direction.
.
A part of a line consisting of two points called end points, and the set of all points between the
end points. A line segment is denoted as
where A and B are the end points.
A point that cuts a line segment into two congruent segments.
Rays with the same endpoint and point in opposite directions. Opposite rays form a line,
A two dimensional object that is infinitely large. Planes have no thickness only length and
width. Planes are named with the word plane followed by three non-collinear points, or by the
word plane followed by a single letter.
A point indicates position. Since it is a place and not a thing, it has no dimension. It has no
length, width, or depth. Points are usually named by a single capital letter.
A closed, coplanar figure made up of 3 or more line segments connected end-to-end.
A polygon such that at least one line containing a side of the polygon contains a point in the
interior of the polygon.
A polygon such that no line containing a side of the polygon contains a point in the interior of
the polygon.
Larson Geometry Reference – Chapter 1
Definitions(Cont.)
Term/Concept
Description
A convex polygon that is both equilateral and equiangular.
Basic assumptions that are accepted as true and do not require proof. Also known as axioms.
A part of a line that starts at an end point goes to infinity in one direction. A ray is denoted
using two points, the end point and some other point on the ray with an arrow over them in one
Polygon, Regular (ch. 7)
Postulates
*Ray
direction
.
Terms that can be combined with other term to make new terms.
Terms that are fundamental and can not be defined using simpler terms. They can only be
described. Point, line, and plane are undefined terms
The point at which line segments, lines or rays intersect in a 2 or 3 dimensional figure.
Terms, Defined
Terms, Undefined
*Vertex
Formulas
Term/Concept
Description
A =  r2
*Circle, Area
*Circle, Circumference
*Distance Formula
The distance between any two points with coordinates (x1,y1) and (x2,y2) is given by the
formula d 
( x 2  x1 ) 2  ( y 2  y1 ) 2
On a number line, the coordinate of the midpoint of a segment whose end points have
*Midpoint Formula
ab
.
2
coordinates a and b is
In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have
coordinates (x1,y1) and (x2,y2) are
Rectangle, Area and Perimeter
Square, Area and Perimeter
Triangle, Area and Perimeter
(
x1  x2 y1  y 2
,
)
2
2
P = 2l + 2w, A = lw
P = 4s, A = s2
P = a+ b + c, A = ½ bh
Postulates
Postulate
*Ruler Postulate(1)
Segment Addition
Postulate(2)
The points on any line can be paired with real numbers so that, given any two points P and Q on the line, P
corresponds to zero, and Q corresponds to a positive number. The distance between the points is the absolute
value of their difference.
If Q is between P and R, then PQ + QR = PR. If PQ + QR = PR, then Q is between P and R.
P
Protractor
Postulate(3)
Angle Addition
Postulate(4)
R
Q
→
Given AB and some number n between 1 and 180, there exists one and only one ray with endpoint A that
→
extends on either side of AB, such that the measure of the angle formed is n.
Given R is in the interior of PQS, then mPQR + RQS = PQS. If PQR + RQS = PQS, then R is in
the interior of PQS.
Theorems
Theorems
Midpoint Theorem
Pythagorean
Theorem
――
――
――
If M is the midpoint of AB , then AM  MB.
In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the
hypotenuse.