Geometry Proofs and Theorems

Segment Addition Postulate

If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC

Same Side Interior Angle Theorem

If two lines are cut by a transversal, the same side interior angles are supplementary

Isosceles Triangle Theorem

If two sides of a ∆ are congruent, then the angles opposite these sides are congruent

No Choice Theorem / 3rd Angles Theorem

If two angles of a ∆ are congruent to two angles of another ∆, then the third angles are congruent

Right Angle Congruence Theorem

If two angles are right angles then they are congruent

Angle Addition Postulate

If you place two angles side-by-side then the measure of the resulting angle will be equal to the sum of the two original angle measures

Perpendicular Line Postulate

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line

Triangle Angle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180º

Congruent Complements Theorem

If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then corresponding angles are congruent

Alternate Interior Angle Theorem

If two lines are cut by a transversal, then alternate interior angles are congruent

Linear Pair Theorem

If two angles form a linear pair, then they are supplements

Triangle Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the non-adjacent ("remote") interior angles of the triangle

Congruent Supplements Theorem

If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent

Converse of the Corresponding Angle Postulate

If two lines are cut by a transversal, and corresponding angles are congruent, then the lines are parallel

Converse of the Alternate Interior Angle Theorem

If two lines are cut by a transversal, and alternate interior angles are congruent, then the lines are parallel

Converse of the Same Side Interior Angle Theorem

If two lines are cut by a transversal, and same side interior angles are supplementary angles, then the lines are parallel

Congruence

Having the same measure

Right Angle

An angle with a measure equal to 90º

Alternate Interior Angles

When two lines are crossed by a transversal, the pairs of angles on opposite sides of the transversal, but inside the two lines

Angle Bisector

A ray that divides an angle into two different congruent angles

Linear Pair

Two adjacent angles whose non - shared rays form a line

Corresponding Angles

Angles at the same location at each intersection

Isosceles Triangle

A ∆ with two congruent sides

Segment Bisector

A segment, line, or plane that intersects a segment at its midpoint

Vertical Angles

Two non - adjacent angles formed by the intersection of the two lines

Same Side Interior Angles

A pair of angles on one side of a transversal line, and on the inside of the two lines being intersected

Base Angle

The side of a triangle from which the height is constructed

Complementary Angles

TWO angles whose measures have a sum of 90º

Supplementary Angles

TWO angles whose measures have a sum of 180º

Alternate Exterior Angles Theorem

If two lines are cut by a transversal, then alternate exterior angles are congruent

Addition Property of Equality

If a = b, then a + c = b + c

Subtraction Property of Equality

If a = b, then a - c = b - c

Multiplication Property of Equality

If a = b, then a • c = b • c

Division Property of Equality

If a = b and c ≠ 0, then a/c = b/c

Substitution Property of Equality

If a = b, then a may replace b in any equation or expression

Reflexive Property

a = a

Symmetric Property

If a = b, then b = a *ONLY EQUALITY*

Transitive Property

If a = b, and b = c, then a = c *ONLY CONGRUENCY*

Distributive Property

a(b + c) = ab + ac

Vertical Angles Theorem

If two angles are vertical angles, then they are congruent

Theorem

A conjecture that is proven

Postulate

An accepted statement of fact

Converse of the Isosceles Triangle Theorem

If two angles of a ∆ are congruent, then the sides opposite the angles are congruent

Conditional

A statement that can be written as "if p, then q" where p and q are two simple statements.