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20 Cards in this Set

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undefined terms

the five primitive terms used as the basis for defining all other geometric terms in plane geometry: point, line, lie on, between, and congruent


an angle with vertex A is a point A together with two distinct non-opposite rays AB and AC emanating from A

between (for rays)

Ray AD is between rays AC and AB if AB and AC are not opposite rays and D is interior to angle CAB.


given distinct points O and A; the set of all points P such that segment OP is congruent to segment OA is called the circle with O as center and OA as radius


Three or more points, A, B,C... are collinear if there exists a line incident with all of them.


Three or more lines, l, m, n,... are concurrent if there exists a point incident with all of them


triangles ABC and DEF are congruent if there exists a one-to-one correspondence between their vertices such that corresponding sides are congruent and corresponding angles are congruent

interior (of an angle)

given an angle CAB, define a point D to be in the interior of angle CAB if D is on the same side of line AC as B and if D is also on the same side of line AB as C. Thus, the interior of an angle is the intersection of two half-planes

interior (of a triangle)

the interior of a triangle is the intersection of the interiors of its three angles. A point is exterior to the triangle if it is not in the interior and does not lie on any side of the triangle

opposite rays

Rays AB and AC are opposite if they are distinct, if they emanate from the same point A, and if they are part of the same line, line AB=line AC

opposite sides (of a line, for two points)

let l be any line, and A and B any points that do not lie on l; if A doesn't= B and segment AB does intersect l, we say that A and B are on opposite sides of l.


lines l and m are parallel if they are distinct lines and no point is incident with both of them


lines l and m are perpendicular if they intersect at a point A and if there is a ray AB that is part of l and a ray AC that is part of m such that angle BAC is a right angle


The ray AB is the following set of points lying on the line AB: those points that belong to the segment AB and all points C on line AB such that B is between A and C. The ray AB is said to emanate from the vertex A and be part of line AB.

right angle

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

same side (of a line, for two points)

let l be any line, and A and B any points that do not lie on l; if A=B or if segment AB contains no point lying on l, we say A and B are on the same side of l


given distinct points A and B; the segment AB is the set whose members are the points A and B and all points C that lie on line AB and are between A and B. The two given points A and B are called endpoints of the segment AB

supplementary angles

If two angles DAB and CAD have a common side ray AD and the other tow sides ray AB and ray AC form opposite rays, the angles are supplements of each other, or supplementary angles

< (for segments)

AB< CD (or CD>AB) means that there exits a point E between C and D such that AB is congruent to CE

< (for angles)

Angle ABC < angle DEF means there is a ray EG between ray ED and ray EF such that angle ABC is congruent to angle GEF