What is the missing reason for the second step in the proof below? R
Given: T is the midpoint of QR
U is the midpoint of RS
T
U
Preve: AQRS - TRU
Q
$
STATEMENTS
REASONS
Gven
?
.
Substitution and simplification
1. T is the midpoint of OR
U is the midpoint of RS
2.
TR = OT TR+QT = OR
RU US, RUUS - RS
OR - OTTR=TR TR = 2TR
RS = RUUS - RU-RU = 2RU
OR RT RT
4.
RS 2RU RU
OR
RT
RU
6. QRSZTRU
ATRU
Division property of equality,
simplification
Property of proportion from
interchangeability
5.RS
Reflexive property
SAS similarity postulate
2. AORS
A. Definition of a midsegment
B. Substitution
C. Definition of a midpoint
D. Simplification