Foundations of Geometry (Vocab)
Geometry is a branch of mathematics concerned with the properties,
position, measurement, and relationships of points, lines, angles, planes, and
solids.
Point – A location in space. A point has no dimensions – no length, no
width, no height. It only has position. We represent a point as a dot and
usually name it with a capital letter such as point P.
P
Line – An infinite set of points with no endpoints. A straight line extends
endlessly in two opposite directions. A line has only one dimension, length.
We can name a line by any two points on it. For example, if two points are A
and B, we have line AB or AB. We can also name a line by a single
lowercase letter, line l.
Plane – A set of points forming a flat surface that extends infinitely in all
directions. A plane has two dimensions, length and width. It has no
thickness.
Collinear Points – A set of points all lying on the same line. ( noncollinear
points do not all lie on the same line.) Any two points are collinear.
Coplanar points – A set of points all lying in the same plane. (Noncoplanar
points do not all lie in the same plane) Any three points are coplanar.
Ray – Part of a line, consisting of one endpoint and all the points on one side
of that endpoint. A ray is named by the endpoint and any other point. We
can refer to the figure as ray AB or AB.
Line segment – Part of a line, consisting of two endpoints and all the points
on the line between them. A line segment is named by the two endpoints. If
the endpoints are A and B, we have line segment AB or AB or BA. The
measure of the length of the segment is the distance between A and B.
Angle – (  ) An angle is formed by two rays that share an endpoint. The rays
are called sides and the endpoint is called the vertex. We can also say that
angles are formed by intersecting lines – lines that cross or meet. In this case
the vertex is the point of intersection.
- There are several ways to name an angle:
1) By a capital letter that names its vertex, such as B
2) By a lowercase letter or a number placed inside the angle, such
as xor1
3) By three capital letters, such as ABC . The middle letter is the
vertex, and the other two letters name points on different rays (or
lines), in either order. ABC can also be named CBA .
- Angles are measured by degrees and are classified by their
measure.
- Congruent angles are equal in measure.
Classification of Angles:
1) Right angle – An angle of exactly 90 degrees. The symbol of a right angle
is a square at the vertex.
2) Acute angle – An angle less than 90 degrees.
3) Obtuse angle – An angle greater than 90 degrees but less than 180
degrees.
4) Straight angle – an angle of exactly 180 degrees. A straight angle is a line.
5) Reflexive angle - an angle whose measure is greater than 180˚ and less
than 360˚.
Adjacent angles – Two angles having the same vertex and sharing one side,
but do not have any interior points in common.
<ABD and <DBC are adjacent
C
D
A
B
Angle bisector – a ray (or any part of a line) whose endpoint is the vertex of
the angle and divides the angle into two congruent (equal) angles.
<ABD = <DBC
A
D
B
C
Complementary angles - two angles whose sum measures 90 degrees.
Supplementary angles - two angles whose sum measures 180 degrees.
(Two angles that create a straight line - a linear pair)
Perpendicular lines ( ) - two lines (or parts of lines) that intersect to form
right angles. Lines with negative reciprocal slopes are perpendicular.
Vertical angles - angles formed by intersecting lines; they are opposite each
other and are congruent