Question

OUT THEOREMS

In a trapezium ABCD , AB || CD , the point P and and the point Q lie on the side AB and BC respectively. PQ || AC , prove that area of trangle ADP AND TRIANGLE ACQ

Answer 1

Given : In a trapezium ABCD , AB || CD , the point P and and the point Q lie on the side AB and BC respectively. PQ || AC ,

To Find :  prove that area of tringle ADP  =   area of tringle ACQ

Solution:

the point P and and the point Q lie on the side AB and BC respectively.

PQ || AC

=> AP/ PB  = CQ/ QB   using BPT / Thales theorem

or AP/AB  = CQ/ BC

h is distance between AB and CD

Area of  Δ ADP  = (1/2) * AP  * h  

Area of  Δ ABC

= (1/2) * AB * h

Area of  Δ ACQ  =   (CQ/BC)  * Area of  Δ ABC

=>  Area of  Δ ACQ  =  (CQ/BC)  * (1/2) * AB * h

CQ/BC  = AP/AB

=>  Area of  Δ ACQ  =  (AP/AB)  * (1/2) * AB * h

=> Area of  Δ ACQ  =   (1/2) * AP * h

=> Area of  Δ ACQ  = Area of  Δ ADP

QED

Hence proved

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