Chapter 4 Review

Cut-n-Paste Proofs

Statements Reasons

X

C

D

B

A SAS PostulateX is midpoint of AC

Definition of Midpoint

BXADXC

DXBX

GivenVertical Angles Theorem

X is midpoint of BDBXADXC

XCAX

Statements Reasons

S

V

TU

R 90R

RSVR

Substitution property

Vertical Angles TheoremUSTRSV

ASA PostulateGivenSUUT

CPCTC90U

Definition of PerpendicularUR

TUVR

USTRSV

USRS

Statements Reasons

C

A

DE

B

CEBC GivenDEAB ||

AAS Theorem

EB

AD bisects BE

Alternate Interior Angles Theorem

Definition of BisectorDA

DECABC

Statements Reasons

O M

L

N

NMOLMO

NMLM

SAS Postulate

CPCTCReflexive Property

NL

OM bisects /LMN

OMOM

GivenNMOLMO

Definition of Bisector

statements reasons

O

M PN ONMONP Definition of Bisector

90ONM

Substitution Property

MPNO

Given

Definition of Perpendicular

NO bisects /POM

Reflexive Property

ASA Postulate90ONP

NONO

PNOMNO

MONPON

statements reasons

KM R

G

Defintion of Midpoint

GKGK

ΔMGR is an isosceles triangle with vertex /MGR

Definition of Isosceles Triangle

GRMG

RGKMGK

Reflexive Property

Given

K is the midpoint of MR

KRMK

SSS Postulate