Foundations of Geometry (Vocab)

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.

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

2) By a lowercase letter or a number placed inside the angle, such as

3) By three capital letters, such as . The middle letter is the vertex, and the other two letters name points on different rays (or lines), in either order. can also be named .

-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.

C

D

AB

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