Angle Proofs

Definition of Congruence

Definition of Congruence

m < A = m<B <--> <A ≅ <B

interior angles

angles locates on the transversal between two specific lines

Definition of Angle Bisector

An angle bisector divides an angle into equal parts.

exterior angles

angles located on the transversal outside two specific lines

Vertical Angles

Across from another angle

Definition of Complementary Angles

Complementary <--> Sum is 90 degrees

Supplementary Angles

2 or more angles on a straight line that add up to 180

Definition of Supplementary Angles

Supplementary <-> Sum is 180 degrees

Complimentary Angles

2 or more angles that add up to 90

Definition of Perpendicular

Perpendicular lines form right angles

Adjacent Angles

share one side and same vertex

Definition of a Right Angle

A right angle = 90 degrees

Alternate Interior Angles

Angles on the inside but opposite sides

Alternate Exterior Angles

Angles on the outside but opposite sides

Angle Addition Postulate

m<ABD + m<DBC = m<ABC

Vertical Angles Theorem

If two angles are vertical, then they are congruent

corresponding angles

Angles that are on the inside or outside and on the same side

Complement Theorem

If two angles form a right angle, then they are complementary. Right Angle --> Complementary

Transversal

A line that intercepts through two or more lines creating multiple angles

Supplement Theorem

If two angles form a linear pair, they are supplementary. Linear pair ---> Supplementary

linear pair

two adjacent angles where the non common side is an opposite ray

Congruent Complements Theorem

If <A is complementary to <B and <C is complementary to <B, then <A ≅ <C

Same Side exterior

exterior angles that lie on the same side of the transversal

Congruent Supplements Theorem

If <A is supplementary to <B and <C is supplementary to <B, then <A ≅ <C