Geometry Definitions and Theorems

A set of flashcards covering important definitions and theorems in geometry.

Linear Pair

Two angles that form a linear pair are adjacent and their sum is 180 degrees.

Supplementary Angles

Two angles whose sum equals 180 degrees.

Complementary Angles

Two angles whose sum equals 90 degrees.

Bisector

A line or segment that divides something into two equal parts.

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 ac=bc for any c.

Division Property of Equality

If a=b, then a/c=b/c for any c≠0.

Square Root Property of Equality

If a=b, then √a=√b.

Distributive Property

a(b+c) = ab + ac.

Substitution Property

If a=b, then a can be replaced with b.

Transitive Property

If a=b and b=c, then a=c.

Reflexive Property

Any quantity is equal to itself, a=a.

Symmetric Property

If a=b, then b=a.

Supplements Theorem

If two angles form a Linear Pair, then they are supplementary.

Segment Addition Postulate

If Point B is between Point A and Point C, then AB + BC = AC.

Angle Addition Postulate

The measures of two adjacent angles sum to the measure of the larger angle.

Midpoint Theorem

If M is the midpoint of AB, then AM = MB.

Congruent Supplements Theorem

If two angles are both supplementary to a third angle, then the two angles are congruent.

Congruent Complements Theorem

If two angles are both complementary to a third angle, then the two angles are congruent.

Vertical Angles Theorem

Vertical angles are congruent.

Parallel Postulate

Through a point not on a line, there is exactly one line parallel to the original line.

Perpendicular Postulate

Through a point not on a line, there is exactly one line perpendicular to the original line.

Corresponding Angles Theorem

If two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

Alternate Interior Angles Theorem

If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.

Alternate Exterior Angles Theorem

If two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.

Consecutive Interior Angles Theorem

If two parallel lines are intersected by a transversal, then the consecutive interior angles are supplementary.

Triangle Angle Sum Theorem

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

Exterior Angles Theorem

An exterior angle of a triangle is equal to the sum of its remote interior angles.

SSS Congruence Postulate

If all three sides of two triangles are equal, then the triangles are congruent.

SAS Congruence Postulate

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

ASA Congruence Postulate

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

AAS Congruence Postulate

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

CPCTC

If two triangles are congruent, then all their corresponding parts are congruent.

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector, it is equidistant from the endpoints of the segment.

Angle Bisector Theorem

If a point is on the angle bisector, it is equidistant from the sides of the angle.