Term
Definition
Chapters 1-5
An angle with a measure between 0 and 90
A triangle with three acute angles
Two angles with a common vertex and side but no common interior points
Two angles that are formed by two lines and a transversal and that lie outside the
two lines on opposite sides of the transversal
Alternate Interior Angles
Two angles that are formed by two lines and a transversal and that lie between the
two lines on opposite sides of the transversal
Altitude of a Triangle
The perpendicular segment from a vertex of a triangle to the opposite side or to
the line that contains the opposite side
Angle Bisector
A ray that divides an angle into two adjacent angles that are congruent
Angle Bisector of Triangle A bisector of an angle of the triangle
Base (Isosceles Triangle)
The noncongruent side of an isosceles triangle that has only two congruent sides
Base Angles (Isos. Tri.)
The two angles that contain the base of an isosceles triangle.
Centroid
The point of concurrency of the medians of a triangle
Circumcenter
The point of concurrency of the perpendicular bisectors of a triangle
Collinear Points
Points that lie on the same line
Complementary Angles
Two angles whose measures have the sum 90
Concurrent Lines
Three or more lines that intersect in the same point
Congruent Segments
Segments that have the same length
Congruent Angles
Angles that have the same measure
Congruent Figures
Two geometric figures that have exactly the same size and shape. When two
figures are congruent, all pairs of corresponding angles and corresponding sides
are congruent. The symbol for “is congruent” is 
Consecutive Interior Angles Two angles that are formed by two lines and a transversal and that lie between the
two lines on the same side of the transversal
Coplanar Points
Points that lie on the same plane
Corresponding Angles
Two angles that are formed by two lines and a transversal and occupy
corresponding positions
Corresponding Angles of Congruent Figures When two figures are congruent, the angles that are in
corresponding positions and are congruent
Corresponding Sides of Congruent Figures When two figures are congruent, the sides that are in
corresponding positions and are congruent
Distance from a Point to a Line The length of the perpendicular segment from the point to the line
Equiangular Triangle
A triangle with three congruent angles
Equidistant from Two Points
The same distance from one point as from another point
Equidistant from Two Lines
The same distance from one line as from another line
Equilateral Triangle
A triangle with three congruent sides
Exterior Angles (Triangle) When the sides of a triangle are extended, the angles that are adjacent to the
interior angles
Hypotenuse
In a right triangle, the side opposite the right angle
Incenter
The point on concurrency of the angle bisectors of a triangle
Interior Angles (Triangle)
When the sides of the triangle are extended, the three original angles of the
triangle
Isosceles Triangle
A triangle with at least two congruent sides
Legs (Isosceles Triangle)
The two congruent sides of an isosceles triangle that has only two congruent sides
Legs (Right Triangle)
In a right triangle, the sides that form the right angle
Acute Angle
Acute Triangle
Adjacent Angles
Alternate Exterior Angles
Linear Pair
Median of a Triangle
Two adjacent angles whose noncommon sides are opposite rays
A segment whose endpoints are a vertex of the triangle and the midpoint of the
opposite side
Midpoint
The point that divides, or bisects, a segment into two congruent segments.
Midsegment of a Triangle A segment that connects the midpoints of two sides of a triangle
Obtuse Angle
An angle with measure between 90 and 180
Obtuse Triangle
A triangle with one obtuse angle
Orthocenter
The point of concurrency of the lines containing the altitudes of a triangle
Parallel Lines
Two lines that are coplanar and do not intersect
Perpendicular Lines
Two lines that intersect to form a right angle
Perpendicular Bisector
A segment, ray, line, or plane that is perpendicular to a segment at its midpoint
Perpendicular Bisector of Triangle A line, ray, or segment that is perpendicular to a side of a triangle at the
midpoint of the side
Point of Concurrency
The point of intersection of concurrent lines
Right Angle
An angle with a measure equal to 90
Right Triangle
A triangle with one right angle
Scalene Triangle
A triangle with no congruent sides
Segment Bisector
A segment, ray, line, or plane that intersects a segment at its midpoint
Skew Lines
Two lines that do not intersect and are not coplanar
Straight Angle
An angle with measure equal to 180
Supplementary Angles
Two angles whose measures have the sum 180
Transversal
A line that intersects two or more coplanar lines at different points
Vertex of a Triangle
Each of the three points joining the sides of a triangle
Vertex Angle (Isos. Tri.)
The angle opposite the base of an isosceles triangle
Vertical Angles
Two angles whose sides form to pairs of opposite rays
Postulates
Segment Addition Postulate
Angle Addition Postulate
Linear Pair Postulate
Parallel Postulate
If B is between A and C , then AB  BC  AC
If P is in the interior of RST , then mRSP  mPST  mRST
If two angles form a linear pair, then they are supplementary
If there is a line and a point not on the line, then there is exactly one line through
the point parallel to the given line
Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through
the point perpendicular to the given line
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of
corresponding angles are congruent
Corresponding Angles Converse
If two lines are cut by a transversal so that corresponding angles are
congruent, then the lines are parallel
Slopes of Parallel Lines
Two lines are parallel if and only if they have the same slope
Slopes of Perpendicular Lines
Two lines are perpendicular if and only if their slopes are
opposite/negative reciprocals
SSS Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then
the two triangles are congruent
SAS Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and
the included angle of a second triangle, then the two triangles are congruent
ASA Congruence Postulate If two angles and the included side of one triangle are congruent to two angles
and the included side of a second triangle, then the two triangles are congruent
Properties
Addition Property of Equality
If a  b, then a  c  b  c
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Substitution Property of Equality
Distributive Property
Segment Congruence
Reflexive Property of Congruence
If a  b, then a  c  b  c
If a  b, then ac  bc
If a  b and c  0, then a  c  b  c
For any real number a, a  a
If a  b, then b  a
If a  b and b  c, then a  c
If a  b, then a can be substituted for b in any equation or expression
a  b  c   ab  ac
For any segment AB, AB  AB
Symmetric Property of Congruence If AB  CD, then CD  AB
Transitive Property of Congruence If AB  CD, and CD  EF , then AB  EF
Angle Congruence
Reflexive Property of Congruence For any angle A, A  A
Symmetric Property of Congruence If A  B, then B  A
Transitive Property of Congruence If A  B, and B  C , then A  C
Triangle Congruence
Reflexive Property of Congruence
Every triangle is congruent to itself
Symmetric Property of Congruence
If ABC  DEF , then DEF  ABC
Transitive Property of Congruence
If ABC  DEF and DEF  JKL, then ABC  JKL
Theorems
Right Angle Congruence Theorem
Congruent Supplements Theorem
All right angles are congruent.
If two angles are supplementary to the same angle (or to congruent angles)
then the two angles are congruent
Congruent Complements Theorem If two angles are complementary to the same angle(or to congruent angles)
then the two angles are congruent
Vertical Angles Theorem
Vertical angles are congruent.
Alternate Interior Angles
If two parallel lines are cut by a transversal, then the pairs of alternate
interior angles are congruent
Consecutive Interior Angles
If two parallel lines are cut by a transversal, then the pairs of consecutive
interior angles are supplementary
Alternate Exterior Angles
If two parallel lines are cut by a transversal, then the pairs of alternate
exterior angles are congruent
Perpendicular Transversal
If a transversal is perpendicular to one of two parallel lines, then it is
perpendicular to the other
Alternate Interior Angles Converse If two lines are cut by a transversal so that alternate interior angles are
congruent, then the lines are parallel
Consecutive Interior Angles ConverseIf two lines are cut by a transversal so that consecutive interior angles are
supplementary, then the lines are parallel
Alternate Exterior Angles Converse If two lines are cut by a transversal so that alternate exterior angles are
congruent, then the lines are parallel
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the
measures of the two nonadjacent interior angles
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another
triangle, then the third angles are also congruent
AAS Congruence Theorem
If two angles and a nonincluded side of one triangle are congruent to two
angles and the corresponding nonincluded side of a second triangle, then
the two triangles are congruent
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are
congruent
Converse of Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are
congruent
Hypotenuse-Leg Congruence Th.
If the hypotenuse and a leg of a right triangle are congruent to the
hypotenuse and a leg of a second right triangle, then the two triangles are
congruent
Perpendicular Bisector Theorem If a point is on a perpendicular bisector of a segment, then it is equidistant
from the endpoints of the segment
Converse of Perp. Bisector Th.
If a point is equidistant from the endpoints of a segment, then it is on the
perpendicular bisector of the segment
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the two
sides of the angle
Conv. of Angle Bisector Th.
If a point is in the interior of an angle and is equidistant from the sides of
the angle, then it lies on the bisector of the angle
Concurrency of Perpendicular Bisectors of a Triangle
The perpendicular bisectors of a triangle intersect at a point that is
equidistant from the vertices of the triangle.
Concurrency of Angle Bisectors of a Triangle
The angle bisectors of a triangle intersect at a point that is equidistant fro
the sides of the triangle.
Concurrency of Medians of a Triangle
The medians of a triangle intersect at a point that is two thirds of the
distance from each vertex to the midpoint of the opposite side.
Concurrency of Altitudes of a Triangle
The lines containing the altitudes of a triangle are concurrent.
Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel
to the third side and is half as long.
Exterior Angle Inequality
The measure of an exterior angle of a triangle is greater that the measure
of either of the two nonadjacent interior angles.
Triangle Inequality
The sum of the lengths of any two sides of a triangle is greater than the
length of the third side.