Math (geometry theroms)

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 = ACAngle Addition Postulate: m<ABC + m<CBD = m<ABD

Construction

Two points determine a straight line.

Construction 2

From a given point on (or not on) a line, one and only one perpendicular can be drawn to the line.

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

If two angles form a linear pair, they are supplementary.

Triangle Sum

The sum of the interior angles of a triangle is 180ยบ.

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.

Base Angle Theorem(Isosceles Triangle)

If two sides of a triangle are congruent, the angles opposite these sides are congruent.

Base Angle Converse(Isosceles Triangle)

If two angles of a triangle are congruent, the sides opposite these angles are congruent.

Side-Side-Side (SSS) Congruence

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Side-Angle-Side (SAS) Congruence

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Angle-Side-Angle (ASA) Congruence

If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Angle-Angle-Side (AAS) Congruence

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.