Basic Proportionality Theorem (Thales Theorem) Video Lecture - Class 10

basic proportionality theorem the
theorem states that a line parallel to
one side of a triangle divides the other
two sides proportionally triangle ABC
has a line drawn parallel to BC which
cuts a B and AC at points P and Q
respectively we are required to prove
that AP by PB is equal to aq by QC
construction let Point P divided a B in
the ratio of L is 2 m where L and M are
natural numbers divide a P in L and PV
in M equal parts click on go for the
proof of the theorem
a pea is cut into L equal parts and
lines are drawn through these points
parallel to BC which is nothing but the
construction
therefore a Q is also cut into L equal
parts we know this from the intercept
theorem
similarly QC is cut into m equal parts
AP by PB is equal to L by M since P
divides a B in the ratio L is 2 m
therefore a Q by Q C is equal to L by M
therefore AP by P B is equal to a Q by Q
C thus the basic proportionality theorem
is proved