Answer:

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Step-by-step explanation:

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Heya ,

Given That :

In ∆ABC the line l || side BC line I intersecet

Side AB & side AC in P & Q respectively ( refer the diagram )

To Prove :

AP / PB = AQ / QC

Construction :

Draw a segment PC & segment QB .

Proof :

A ( ∆APQ ) / A ( ∆PBQ ) = AP / PB ┈┈ (Ⅰ)

(Areas that are proportional to the bases)

A (∆PAQ) / A(∆PQB) = AQ / QC ┈┈ (Ⅱ)

(Areas in porportion to the bases)

∆PBQ & ∆ PQC having the same bases PQ & PQ II BC , their height same .

A(∆ PQB ) = A ( ∆ PQC ) ┈┈ (Ⅲ)

∴A(∆APQ) / A(∆PQB) = A(∆APQ) / A(∆PQC) ┈┈ From (Ⅰ), (Ⅱ) & (Ⅲ)

∴ AP / PB = AQ / QC ┈┈ From (I) , (II)

Hence , Proved

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