POINT

undefined term. We will denote points by P, Q, R, etc.

LINE

undefined term. We will denote lines by k, l, m, etc. The unique line that passes through P and Q will be denoted by .

INCIDENCE

undefined relation between a point and a line. We say that "P lies on l", or "l is incident with P", or "l passes through P", and we will use the notation P_Il, or .

PARALLEL

Two lines l and m are parallel if they do not intersect, i.e. no point lies on both of them. We denote this by l||m .

CONCURENT

We say that three lines l, m, and n are concurent if there is a point P that lies on all three lines.

 COLLINEAR

 Points A₁, A₂, …, A_n are collinear if there is a line l such that they all lie on l.

BETWEEN

undefined term. We will use the notation A*B*C to abbreviate the statement " point B is between point A and point C".

SEGMENT

Given two points A and B, we define the segment AB as the set of all points between A and B, together with the endpoints A and B:

RAY

Given two points A and B, we define the ray as the set of all points on the segment AB together with all the points C such that A*B*C: . We say that the ray emanates from A.

OPPOSITE RAYS

Two rays are opposite if they are distinct, if they emanate from the same point, and if they are part of the same line.

SAME SIDE OF A LINE

Let l be a line, and A and B any points that do not lie on l. We say that A and B are on the same side of l if A=B or if segment AB does not intersect l.

OPPOSITE SIDES OF A LINE

Let l be a line, and A and B any points that do not lie on l. We say that A and B are on opposite sides of l if and if segment AB does intersect l.

HALF-PLANE

Expression commonly used for a side of a line.

ANGLE

An angle is a point A (called the vertex of the angle) together with two distinct non-opposite rays emanating from A (called sides of the angle). If and are the two sides of an angle, we will denote the angle by .

INTERIOR OF AN ANGLE

We say that point D is interior to an angle if B and D are on the same side of line , and C and D are on the same side of line .

RAY BETWEEN TWO RAYS

We say that ray is between and , if and are not opposite rays and D is interior to angle .

TRIANGLE

If A, B, and C are non-collinear, then the union of the segments AB, BC, and AC is called a triangle and is denoted by . Segments AB, BC, and AC are called the sides of the triangle, and angles and are the angles of the triangle.

INTERIOR OF A TRIANGLE

The intersection of the interiors of all its three angles.

EXTERIOR OF A TRIANGLE

A point is exterior to a triangle if it is not interior, and does not lie on any side of the triangle.

CONGRUENT SEGMENTS

undefined relation between segments. We will use the notation to denote two congruent segments.

CONGRUENT ANGLES

undefined relation between angles. We will use the notation to denote two congruent angles.

CONGRUENT TRIANGLES

Two triangles are congruent if a one-to-one correspondence can be set up between their vertices such that the corresponding sides are congruent and the corresponding angles are congruent.

SUPPLEMENTARY ANGLES

We say that two angles are supplementary if they have a common side and the other two sides are opposite rays.

VERTICAL ANGLES

Two angles are vertical if the sides of one are opposite to the sides of the other.

RIGHT ANGLE

An angle is a right angle if it has a supplementary angle to which it is congruent.

SEGMENT LESS THAN ANOTHER SEGMENT

We say that AB<CD if there is a point E between C and D such that segments AB and CE are congruent. We also say that CD>AB.

 ANGLE LESS THAN ANOTHER ANGLE

 We say that if there is a ray between and such that .