In fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such that
PQ=RQ,
∠PQT=∠RQU...(i)
∠TQS=∠UQS...(ii)
Prove that: QT=QU.

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Solution

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 [By ASA]

∴QT=QU [By CPCT]

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If Fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such PQ = RQ.
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In fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such that PQ=RQ,∠PQT=∠RQU...(i)∠TQS=∠UQS...(ii)Prove that: QT=QU.

In fig. PQRS is a quadrilateral and T and U are respectively points on PS and RS such that
PQ=RQ,
∠PQT=∠RQU...(i)
∠TQS=∠UQS...(ii)
Prove that: QT=QU.