Basic Geometry and Proofs

lines l and m are perpendicular

<a and <b are adjacent

<a and <b are complementary

m<a = m<b

m<RPL = m<LPQ

<RPL + m<LPQ = m<RPQ

<RPQ is acute

m<RPQ = 90

Addition property

Segment Addition Postulate

Substitution property

Transitive property

<ABC is not an acute angle

<ABC is supplementary to another angle

m<ABC = $$180\degree$$  

<ABC is a straight angle

Symmetric Prop.

Angle addition postulate

Reflexive Prop

Transitive Prop.

that the angles are equal

that the angles add up to 180 degrees

that the angles are a linear pair

that the angles are right angles

Split it into 3 equal parts.

Split it into 2 equal parts.

Split into 4 equal parts.

Double it.

Angles that form a linear pair are supplementary.

Substitution

Reflexive Property of Congruence

Angles of equal measure are congruent.

Angles that form a linear pair are supplementary.

Angles of Equal Measure are Congruent

Reflexive Property of Congruence

Definition of a Perpendicular Bisector

$$AD≅DB$$  

$$CD≅CD$$  

$$m\angle ADC+m\angle BDC=180\degree$$  

$$\angle ADC\cong\angle BDC$$