Question

what is basi proportonality theorem

Answer 1

basic proportionality theorem. if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.


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Answer 2

BASIC PROPORTIONALITY THEOREM
If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

PROOF ======>>>

Given: In ΔABC, DE is parallel to BC
Line DE intersects sides AB and PQ in points D and E, such that we get triangles A-D-E and A-E-C.

To Prove:AD/BD=AE/CE

Construction: Join segments DC and BE

Proof:
In ΔADE and ΔBDE,
area (ADE)/area(BDE) = AD/BE
(triangles with equal heights)

In ΔADE and ΔCDE,
area(ADE)/area(CDE) = AE/EC
(triangles with equal heights)

Since ΔBDE and ΔCDE have a common base DE and have the same height we can say that,
A(ΔBDE)=A(ΔCDE)

Therefore,
area (ADE)/area(BDE) = area(ADE)/area(CDE)

therefore
AD/BE = AE/EC
Hence Proved.

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