Question

In Square ABCD AD||BC ; Diagonal AC &BD interest point 'P' Then show (AD/PD)= PC/BP)​

Answer 1

Answer:

Given:

AD || BC, diagonal AC and diagonal BD intersect each other at point P.

To prove : AP/PD=PC/BP

Construction :

Draw ST || BC

Proof :

AS/SB=DT/TC..............(1)

[By using property of three || lines and their transversals]

In ∆’s ABC & DCB we get,

AS/SB=AP/PC..............(2)

DT/TC=PD/BP..............(3)

[By using basic proportionality theorem]

From eq (1),(2) & (3),

AP/PC=PD/BP

i.e. AP/PD=PC/BP

Hence proved ..

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