PQRS is a parallelogram
with PQ = 15 cm, ST
= 10 cm, and QV = 12 cm.
Find PS.
10 cm
12 cm fi

1 thought on “<br /><br /> PQRS is a parallelogram<br />with PQ = 15 cm, ST<br />= 10 cm, and QV = 12 cm.<br />Find PS.<br />10 cm<br />12 cm fi”

1. Answer:

   Given: PQRS is a parallelogram. PQ=15 and RQ=10, LPRL=32

   In △RLQ and △NLP

   ∠RLQ=∠NLP (vertically opposite angles)

   ∠LRQ=∠LPN (Alternate angles)

   ∠LQR=∠LNP (Alternate angles)

   Thus, △RLQ∼△PLN (AAA rule)

   Hence, PLRL=PNRQ (Corresponding sides of similar triangles)

   PN=23×10

   PN=15cm

   Similarly, △RLM∼△PLQ

   LPRL=PQRM (Corresponding sides of similar triangles)

   RM=315×2

   RM=10 cm.

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