# Geometry Stuff... XD

## This is just some theorems, postulates, properties, and all kinds of other geometry stuff. Enjoy!

Chapter 1.

### 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.

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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