AR+RM=AM and LE+EG=LG - Segment addition

RM+AR=LG and EG+LE=AM - Substitution

LG = MA - Substitution

2) AB=BC and BC=CD - Given

AB = CD Transitive

3) QR=RS - Given

QS = QR + RS - Segment Addition

QS = RS + RS - Substitution

QS = 2RS - Addition

4) AC = AD and AB = AE - Given

AB+BC = AC and AE+ED = AD - Segment addition

AE+ED = AC - Transitive

AB+ED = AC - Substitution

BC = AC-AB and ED = AC-AB - Subtraction

BC = ED - Transitive

5) Segment ABCD - Given

AB + BC = AC - Segment Addition

AC + CD = AD - Segment Addition

AB + BC + CD = AD - Substituion