Identity Postulates
A quantity is congruent (equal) to itself. a = a
Reflexive Property
If equal quantities are added to equal
quantities, the sums are equal.
Addition Postulate
All are congruent, 90 degrees
Right Angles
Created when a transverse cuts another line. Opposites. Congruent
Vertical angles
Point C lies in the interior of !ABD , if and only if,
m!ABC + m!CBD = m"!ABD
Angle Addition Postulate
A quantity may be substituted for its equal
in any expression
Substitution Postulate
If equal quantities are subtracted from
equal quantities, the differences are equal.
Subtraction Postulate
All are congruent, 180 Degrees
Straight angle
If two parallel lines are cut by a transversal, then the pair of angles in identical position are congruent
Corresponding Angles
If two lines are cut by a transversal and the corresponding angles are
congruent, then lines are parallel.
Corresponding Angles
Converse
If a = b and b = c, then a = c.
Transitive Property
If equal quantities are multiplied by equal
quantities, the products are equal.
Multiplication Postulate
Two angles who share a vertex and side, which make a straight angle
Linear Pair
If two parallel lines are cut by a transversal, angles on opposite sides of the transversal and within the parallel lines.
Alternate Interior Angles
If two lines are cut by a transversal and the alternate interior angles are
congruent, then lines are parallel.
Alternate Interior Angles
Converse
The whole is equal to the sum of its parts.
Partition Postulate
If equal quantities are divided by equal
nonzero quantities, the quotients are equal.
Division Postulate
Sum of the interior angles of a triangle
180 degrees
If two parallel lines are cut by a transversal, angles on opposite sides of the transversal and outside the parallel lines.
Alternate Exterior Angles
If two lines are cut by a transversal and the alternate exterior angles are
congruent, then lines are parallel.
Alternate Exterior Angles
Converse
If a = b, then b = a.
Symmetric Property
Point B is a point on segment AC, i.e. B is
between A and C, if and only if AB + BC = AC
Segment Addition Postulate
The measure of an exterior angle of a triangle is
equal to the sum of the measures of the two
non-adjacent interior angles.
Exterior Angle of a triangle
If two parallel lines are cut by a transversal, angles on same side of the transversal and within the parallel lines.
Consecutive or Same Side interior angles
If two lines are cut by a transversal and the interior angles on the same
side of the transversal are supplementary, then lines are parallel.
Interiors on Same Side
Converse