General TheoremsReflexive Property=
A quantity is congruent (equal) to itself. a = a
If a = b, then b = a.
If a = b and b = c, then a = c.
If equal quantities are added to equal quantities, the sums are equal.
If equal quantities are subtracted from equal quantities, the differences are equal.
If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.)
If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.)
A quantity may be substituted for its equal in any expression.
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.
All right angles are congruent.
All straight angles are congruent.
Supplements of the same angle, or congruent angles, are congruent.
Complements of the same angle, or congruent angles, are congruent.
If two angles form a linear pair, they are supplementary.
Vertical angles are congruent.
The sum of the interior angles of a triangle is 180º.
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.