The given figure shows a parallelogram PQRS, ST and QU are the bisectors of ∠PSR and ∠PQR respectively.
If SU = 4 cm and QU = 10 cm, then what is the value of (ST + TQ)?
(A) 12 cm (B) 14 cm (C) 16 cm (D) 18 cm
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PQRS is a parallelogram. ST and QU are the bisectors of ∠ PSR and ∠ PQR and QU = 10 cm and SU = 4 cm .
∠ PSR = ∠ PQR (given)
Since, opposite sides of a parallelogram are parallel,
PQSR
⇒TQSU
Consider ST as transversal,
∠ QTS + ∠ TSU = 180° (angles on the same side of a transversal are supplementary)
Also, ∠ TQU + ∠ SUQ = 180° (angles on the same side of a transversal are supplementary)
Since, ∠TSU = ∠TQU
So, ∠ SUQ = ∠QTS
In quadrilateral TQUS, since a pair of opposite angles are equal and TQSU,
TQUS is a parallelogram.
Hence, TQ = SU and ST = QU
ST + TQ = QU + SU = 10 + 4 = 14 cm.
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