Geometry Theorems and Postulates

Linear Pair Theorem

if two angles form a linear pair then their measure has a sum of 180

Right angle theorem

all right angles are congruent

vertical angles theorem

if two angles are vertical then they are congruent

congruent supplements theorem

if two angles are supplementary to the same angle then they are congruent

congruent compliments theorem

if two angles are complimentary to the same angle then they are congruent

converse of the alternate interior angles theorem

if two lines are cut by a transversal and alternate interior angles are congruent then thee lines are parallel

converse of the alternate-exterior angle theorem

if two lines are cut by a transversal and alternate exterior angles are congruent then the lines are parallel

converse to the same side interior angle theorem

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

converse to the same-side exterior angle theorem

if two line are cut by a transversal and the same side exterior angles are supplementary then the lines are parallel

alternate interior angle theorem

if two parallel lines are cut by a transversal then alternate interior angles are congruent

alternate exterior angle theorem

if two parallel lines are cut by a transversal then the alternate exterior angles are congruent

same side interior angle theorem

if two parallel line are cut by a transversal then same side interior angles are supplementary

same side exterior angle theorem

if two parallel lines are cut by a transversal then same side exterior angles are supplementary

triangle sum theorem

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

right-triangle compliments theorem

the acute angles of a right triangle are complimentary

exterior angle theorem

the measure of exterior angle of a triangle is equal to the sum of the measures of its remote interior angles

quadrilateral sum theorem

the sum of the measure of the interior angles of a quadrilateral is 360

Segment Addition Postulate

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

Angle Addition Postulate

If point D is in the interior of ∠ABC, then m∠ABC, then m∠ABD+m∠DBC=m∠ABC

line postulate

through any two points there is exactly one line

parallel postulate

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

perpendicular postulate

through a point not on a line there is exactly one line perpendicular to the given line

corresponding angles postulate

if two parallel are cut by a transversal, the pairs of corresponding angles are congruent

converse of corresponding angles postulate

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

AAA similarity postulate

if the three angles of one triangle are congruent to the three angles of another triangle, then the two triangles are similar

Linear pair postulate

if two angles form a linear pair then they are supplementary