Question

diagonals ac and bd of a quadrilateral abcd interaect each other at P.show that ar(APB)*ar(cpd)=ar(apd)*ar(bpc)​

Answer 1

TO prove:

Step-by-step explanation:

Given:□ABCD is given in which AB=DC&AD=BC

To prove:ar(APB)and ar(APD) ar(BPC)

Proof:In APB&CPD

AB=DC(given)S

angel APB=angel DPC(V.O.A)A

angel ABP=angel PDC(A.A)A

Thus from A.A.S criteria

APB=CPD EQ-1

From the c.p.c.t of eq.1 ar(APB)=ar(CPD )

In APD&BPC

AD=BC (given)S

angel APD=angel BPC(A)

angel DAP=angel PCB(A)

Thus from A.A.S

arAPD=BPC