5 7. PQRS is a quadrilateral with QR = RS. Prove that a. PQ = PS
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Step-by-step explanation:
RU+ZUQS
In A PQS and A RQS,
PQ=QR (given)
ZPQS=<RQS
[2PQT=2RQU &
ZTQS=ZUQS
..<PQT+2TQS=<RQU+zUQS
ZPQS=<RQS ]
QS=QS [common]
APQT ARQS [BY SAS]
ZPSQ=ZQSR [By CPCT] →(1)
Now, in A QTS A QSU
QS=QS (common)
ZTQS=2SQU [given]
ZTSQ=ZUSQ [from (1)]
:: Δ QTS= Δ QSU
::QT=QU [By CPCT]
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