Math, asked by tanishhadkar, 9 months ago

please answer the above question fast as I have board exam tomorrow​

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Answers

Answered by samijain1069
2

ANSWER:

Given: in quadrilateral ABCD,

AD ║ BC and AP=1/3 AC

TO PROVE: DP=1/2 BP.

Proof:

Since, AP=1/3 AC

⇒ AP/AC = 1/3

Let, AP = x and AC = 3x

Where x is any number,

⇒ CP = AC - AP = 3x - x = 2x

Now, In quadrilateral ABCD,

AD ║ BC

By the Alternative interior angle theorem,

∆PAD=~∆PCB

AND ∆PDA=~∆CPB

By property of similar triangle,

AB/PD=CP/PB

X/PD=2X/PB

PB/PD=2/1

PD/PB=1/2

PD=1/2×PB

DP=1/2×BP

Hence proved

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