Proofs in Geometry

Angles that form a linear pair are supplementary. $$m∠1+m∠3=180°$$  

$$m∠3+m∠5=180°$$  

$$m∠1=m∠3$$  

$$\angle3\cong\angle5$$  

SSS

SAS

ASA

The triangles are not congruent.

SSS

SAS

ASA

Not Congruent

Reflexive Property of Congruence

Corresponding Parts of Congruent Triangles are Congruent

Angles that form a linear pair are supplementary.

Alternate Interior Angles are Congruent.

Addition property

Segment Addition Postulate

Substitution property

Transitive property

AB + BC = AC

AB = BC

A is the segment bisector of BC

ABC is a straight angle

<ORP is a right angle

QR + RP = QP

<ORQ and <ORP are complementary

<QRP = 180 $$\degree$$  

<1 and <2 are a linear pair

<1 and <3 are right angles

<2 and <4 are vertical angles

$$<1\cong<3$$  

m<1 + m<2 = 180

m<1 + m<2 = 90

m<1 = m<2

nothing

Angle addition postulate

Definition of straight angle

Linear Pair Postulate

Definition of supplementary