Question

basic proportionality theorm step by step proof pls

Answer 1

hope you understand that
and it may help you

Answer 2

Given: A ΔABC in which line DE is parallel to BC

Line DE intersects sides AB and AC in two distinct points D and E respectively.

To Prove that : AD/BD=AE/CE

Construction: Draw EF ⟂ AD and DG⟂ AE and join the segments BE and CD.

Proof:  

Area of Triangle= ½ × base× height  ( Formula)

In ΔADE and ΔBDE,

Ar(ADE)/Ar(DBE)=1/2×AD×EF/1/2×DB×EF=AD/DB (Equation.....1)

In ΔADE and ΔCDE,

 

Ar(ADE)/Ar(ECD)=1/2×AE×DG/1/2×EC×DG = AE/EC (Equation -------2)

Note that ΔDBE and ΔECD have a common base DE and lie between the same parallels DE and BC. Also, we know that triangles having the same base and they are lying between the same parallels are equal in area.

So, we can say that

Ar(ΔDBE)=Ar(ΔECD)

Therefore,

A(ΔADE)Ar(ΔBDE)=Ar(ΔADE)Ar(ΔCDE)

Therefore,

AD/BD=AE/CE

Hence Proved.