Geometry Chapter 2 Definitions, Theorems, & Postulates

Symmetric Property of Equality

• If a = b, then b = a.

• If a + b = c, then b + a = c.

• If AB = CD, then AB = CD.

• If m∠A = m∠B, then m∠C = m∠A.

Definition of Supplementary Angles

• If @@\angle 1@@ and @@\angle 2@@ are supplementary angles, then @@m\angle 1 + m\angle 2 = 180^\circ@@.

• If @@\angle 1@@ and @@\angle 2@@ are complementary angles, then @@m\angle 1 + m\angle 2 = 90^\circ@@.

• If @@\angle 1@@ and @@\angle 2@@ are adjacent angles, then @@m\angle 1 + m\angle 2 = 360^\circ@@.

• If @@\angle 1@@ and @@\angle 2@@ are vertical angles, then @@m\angle 1 = m\angle 2@@.

Definition of Angle Bisector

• If @@\overrightarrow{BD}@@ bisects @@\angle ABC@@, then @@\angle ABD \cong \angle DBC@@

• If @@\overrightarrow{BD}@@ is perpendicular to @@\angle ABC@@, then @@\angle ABD \cong \angle DBC@@

• If @@\overrightarrow{BD}@@ is an extension of @@\angle ABC@@, then @@\angle ABD \cong \angle DBC@@

• If @@\overrightarrow{BD}@@ divides @@\angle ABC@@ into two unequal parts, then @@\angle ABD \cong \angle DBC@@

Reflexive Property of Equality

• a = a

• a + b = b + a

• AB = BA

• m\angle A \neq m\angle B

Right Angles Theorem

• If @@\angle 1@@ and @@\angle 2@@ are right angles, then @@\angle1\cong\angle2@@

• If @@\angle 1@@ is a right angle, then @@\angle 2@@ is acute.

• If @@\angle 1@@ and @@\angle 2@@ are complementary, then @@\angle1\cong\angle2@@

• If @@\angle 1@@ is obtuse, then @@\angle 2@@ is also obtuse.

Angle Addition Postulate

• If @@\angle ABC@@ and @@\angle CBD@@ are adjacent, then @@m\angle ABC+m\angle CBD=m\angle ABD@@

• If @@\angle ABC@@ and @@\angle CBD@@ are complementary, then @@m\angle ABC+m\angle CBD=90^\circ@@

• If @@\angle ABC@@ and @@\angle CBD@@ are supplementary, then @@m\angle ABC+m\angle CBD=180^\circ@@

• If @@\angle ABC@@ and @@\angle CBD@@ are vertical angles, then @@m\angle ABC=m\angle CBD@@

Distributive Property

• a(b + c) = ab + ac

• a(b + c) = a + bc

• ab + ac = a(b + c)

• a(b + c) = ab - ac

If @@\angle 1@@ and @@\angle 2@@ are a linear pair, then what is the relationship between their measures?

• @@m\angle1 + m\angle2 = 90\degree@@

• @@m\angle1 + m\angle2 = 180\degree@@

• @@m\angle1 + m\angle2 = 360\degree@@

• @@m\angle1 + m\angle2 = 45\degree@@

Symmetric Property of Congruence

• If @@\angle A \cong \angle B@@, then @@\angle B \cong \angle A@@

• If @@\angle A \cong \angle C@@, then @@\angle C \cong \angle B@@

• If @@\angle A \cong \angle B@@, then @@\angle A \cong \angle C@@

• If @@\angle B \cong \angle A@@, then @@\angle A \cong \angle D@@

Vertical Angles Theorem

• If @@\angle 1@@ and @@\angle 2@@ are vertical angles, then @@\angle1\cong\angle2@@

• If @@\angle 1@@ and @@\angle 2@@ are complementary angles, then @@\angle1 + \angle2 = 90^\circ@@

• If @@\angle 1@@ and @@\angle 2@@ are supplementary angles, then @@\angle1 + \angle2 = 180^\circ@@

• If @@\angle 1@@ and @@\angle 2@@ are adjacent angles, then @@\angle1 + \angle2 = 360^\circ@@