PQRTS is a Pentagon. A line through T meets QR prouduced in U such that SR || UT. Show that ar(PSUQ)=ar(PQRTS)
Answer
Text Version of the Answer is
Q -PQRTS is a pentagon A line Through t meels ar (PSUQ) = ar (PQRTS)
Q R U
X S T
In fig, ∆ STR and ∆ RTS are on the same base RS and between parallel lines RS ∥ VT (given)
∴ ar (∆ STR) = ar (∆ RTS) …….(1)
Now, ar (PSVQ) = ar (PSRQ) + ar (∆ STR)
= ar (PSRQ) + ar (∆RTS)
(From (1))
ar (PQRTS)
∴ ar (PSVQ) = ar (PQRTS)