Question

What is the missing reason for the second step in the proof below?RGiven: Tis the midpoint of QRU is the midpoint of RSTUProve: AQRS - ATRUQSREASONSGiven?Substitution and simplificationSTATEMENTS1. Tis the midpoint of ORU is the midpoint of RS2.TR =ỘT TR+QT = QRRU US, RU-US - RS3. OR - QT +TR-TR+TR = 2TRRS = RU +US RU + RU=2RUOR 2RT RT2RU RUOR RTRU6. ZORSE ZTRU7AORSATRU4. RSDivision property of equality,simplificationProperty of proportion fromInterchangeabilityReflexive propertySAS similarity postulate5. RS

Answer 1

The second statement in the given proof is

$\begin{gathered} \bar{TR}\cong\bar{QT},\: \bar{TR}+\bar{QT}\bar{=QR} \\ \bar{RU}\cong\bar{US},\: \bar{RU}+\bar{US}\bar{=RS} \end{gathered}$

Since we are given that T is the midpoint of QR which makes TR equal to QT and the sum of TR and QT must be equal to QR as per the definition of a midpoint

Similarly, we are given that U is the midpoint of RS which makes RU equal to US and the sum of RS and US must be equal to RS as per the definition of a midpoint

Therefore, the correct answer is "definition of a midpoint"