Question

hi everyone pls prove Converse bpt​

Answer 1

Answer:

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,

DBAD = ECAE ______ (1)

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

Thales theorem,

DBAD = FCAF _______ (2)

Simplify (1) and (2)

ECAf = FCAF

adding 1 on both sides

ECAE +1= FCAF +1

⇒

ECAE+EC = FCAF+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.

Answer 2

hope this will help you

please mark me as brainliest