Math Review

Substitution

Replacing

e.g m<2 with m<3 if m<1 + m<2 = 100° then m<1 + m<3 = 100°

Reflexive Property

Same on both sides, e.g., bc = bc

Symmetric Property

Flip around equal sign, e.g., if a = b, then b = a

Transitive Property

If m<1 = m<2 and m<2 = m<3, then m<1 = m<3

Congruent Complements Theorem

If two angles are complementary to the same angle, then the two angles are congruent.

Right Angles Congruence Theorem

All right angles are congruent.

Congruent Supplementary Angles Theorem

If two angles are supplementary and are equal measurements then angles are congruent.

Linear Pair Theorem

If a linear pair, then supplementary.

Adjacent Angles Theorem

If adjacent and forms right angle, then complementary.

Congruent Supplements Theorem

If two angles are supplementary to the same angle, then those two are congruent.

Vertical Angle Theorem

Vertical angles are congruent.

Definition of Right Angle

An angle that measures exactly 90 degrees.

Definition of Acute Angle

An angle that measures greater than 0 degrees and less than 90 degrees.

Definition of Obtuse Angle

An angle that measures greater than 90 degrees and less than 180 degrees.

Definition of Complementary Angles

Two angles that sum to 90 degrees exactly.

Definition of Supplementary Angles

Two angles that sum to 180 degrees exactly.

Definition of Angle Bisector

A line, ray, or line segment that divides an angle into two equal, congruent smaller angles.

Definition of Midpoint

Exact middle of a line segment.