Question

PQRS is a quadrilateral where PQ=RQ, angle PQT=RQU and angle RQS=UQS. prove that I) triangle PQSis congruent to triangle RQS ii) QT=QU​

Answer 1

Answer:

RU+∠UQS

In △PQS and △RQS,

PQ=QR (given)

∠PQS=∠RQS

[ ∵∠PQT=∠RQU &

∠TQS=∠UQS

∴∠PQT+∠TQS=∠RQU+∠UQS

∠PQS=∠RQS ]

QS=QS [common]

∴△PQT≅△RQS [By SAS]

∠PSQ=∠QSR [By CPCT] →(1)

Now, in △QTS △QSU

QS=QS (common)

∠TQS=∠SQU [given]

∠TSQ=∠USQ [from (1)]

∴△QTS≅△QSU

∴QT=QU [By CPCT]