Question

In the adjoining figure ABCD is a trapezium in which AB is parallel to DC. O is the mid point of BC. Through the point o a line QP parallel to AD has been drawn which intersects AB at Q and DC produced At p prove that ar(ABCD)=ar(AQPD)

Answer 1

Answer:

Step-by-step explanation:

Given: ABCD is a trapezium with AB||CD 

L is the midpoint of BC and PQ || AD 

 Now in ΔCLQ and  ΔBLP 

∠LCQ = ∠LBP 

CL = BL ( L is the midpoint of BC) 

∠CLQ = ∠BLP 

So ΔCLQ = ΔBLP 

Area (ΔCLQ) = Area (ΔBLP) 

Area (ABCLP) + Area (ΔCLQ) = Area (ADCLP) + Area (ΔBLP) 

So area (APQD) = Area (ABCD)

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