Question

state and prove converse of BPT

Answer 1

hope this answer will help you.

Answer 2

Answer:

REF.Image

Converse of Basic proportionality Theorem

Statement : If a line divide any two sides of a triangle (Δ) in the same ration, then the line must be parallel (||) to third side.

If

DE

AD

=

EC

AE

then DE||BC.

Prove that : DE||BC.

Given in ΔABC, D and E are two points of AB and AC respectively, such that,

DB

AD

=

EC

AE

______ (1)

Let us assume that in ΔABC, the point F is an intersect on the side AC. So, we can apply the

Thales theorem,

DB

AD

=

FC

AF

_______ (2)

Simplify (1) and (2)

EC

AE

=

FC

AF

adding 1 on both sides

EC

AE

+1=

FC

AF

+1

⇒

EC

AE+EC

=

FC

AF+FC

⇒

EC

AC

=

FC

AF

⇒AC=FC

From the above we can sat that the points E and F are coincide on AC, i.e., DF coincides with DE. Since DF is parallel to BC, DE is also parallel to BC.

∴ Hence, the converse of Basic proportionality Theorem is proved