Question

PQRTS is a pentagon. A line through T meets QR produced in U such that SR || UT. Show that ar ( PSUQ) =ar (PQRTS).

Answer 1

Given : ABCDE is a Pentagon.

Construction : join AF anf BC

Proof :

(1)

Since triangles ACD
and triangle ACF

are on the same base AC and between the same parallels AC and BF. So,

ar ( triangle ACD)= ar (triangle ACF)

hence proved.

(2)

now
ar ( triangle ACD)= ar ( triangle ACF)
adding ar (ACDE) both sides we get,
ar( triangle ACB) +ar (ACDE)= ar (triangle ACF)+
ar (ACDE).
=> ar ( ABCDE)= ar(AEDF)

Hence Proved.