Question

In □ ABCK seg BC ll seg AD. Diagonols AC and BD interset each other at point P.If AP = 1/3(AC),then prove that DP = 1/2 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 ..

Answer 2

see solution in image .....