ABCD is a //gm and ar ( BCP )  = ar ( DPQ )  . Prove that ar ( BPC ) = ar ( DPQ) , provided BC = CQ  ( P[LS EXPERTS ANS URGENTLY )

Asked by Vikas | 18th Jan, 2018, 12:19: AM

Expert Answer:

begin mathsize 16px style triangle APC space and space triangle BPC space are space on space the space same space base space PC space and space between space the space same space parallels space PC space and space AB.
rightwards double arrow straight A left parenthesis triangle APC right parenthesis equals straight A left parenthesis triangle BPC right parenthesis space space space space space.... left parenthesis straight i right parenthesis
ABCD space is space straight a space aparallelogram.
rightwards double arrow AD equals BC
rightwards double arrow AD equals QC space space space space space left parenthesis given space BC equals CQ right parenthesis
In space quadrilateral space ADQC comma space AD equals QC space and space AD parallel to QC.
rightwards double arrow ADQC space is space straight a space parallelogram.
rightwards double arrow AP equals PQ space and space CP equals PD
In space triangle APC space and space triangle DPQ comma
AP equals PQ
angle APC equals angle DPQ
PC equals PD
rightwards double arrow triangle APC approximately equal to triangle DPQ space space space space left parenthesis SAS space congruence right parenthesis
rightwards double arrow Area space left parenthesis triangle APC right parenthesis equals Area space left parenthesis triangle DPQ right parenthesis space space space.... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma
Area space left parenthesis BCP right parenthesis equals Area space left parenthesis triangle DPQ right parenthesis end style

Answered by Rashmi Khot | 18th Jan, 2018, 10:45: AM