prove the converse of BPT
Answers
Answer:
State and prove converse of BPT.
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.
Given in ΔABC, D and E are two points of AB and AC respectively, such that,
Let us assume that in ΔABC, the point F is an intersect on
Answer:
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.
