General Theorems
Reflexive Property=A quantity is congruent (equal) to itself. a = a
Symmetric Property=
If a = b, then b = a.
Transitive Property=
If a = b and b = c, then a = c.
Addition Postulate=
If equal quantities are added to equal quantities, the sums are equal.
Subtraction Postulate=
If equal quantities are subtracted from equal quantities, the differences are equal.
Multiplication Postulate=
If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.)
Division Postulate=
If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.)
Substitution Postulate=
A quantity may be substituted for its equal in any expression.
Partition Postulate=
The whole is equal to the sum of its parts.
Also: Betweeness of Points: AB + BC = AC
Angle Addition Postulate: m<ABC + m<CBD = m<ABD
Construction Two points determine a straight line.
Construction From a given point on (or not on) a line, one and only one perpendicular can be drawn to the line.
Angles:
Right Angles=
All right angles are congruent.
Straight Angles=
All straight angles are congruent.
Congruent Supplements=
Supplements of the same angle, or congruent angles, are congruent.
Congruent Complements=
Complements of the same angle, or congruent angles, are congruent.
Linear Pair=
If two angles form a linear pair, they are supplementary.
Vertical Angles=
Vertical angles are congruent.
Triangle Sum=
The sum of the interior angles of a triangle is 180º.
Exterior Angle=
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
The measure of an exterior angle of a triangle is greater than either non-adjacent interior angle.
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