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3 The Side

Splitting Theorem
Side

Splitting Theorem:
If a line is parallel to a side of a triangle and intersects the
other two sides in distinct points, it splits these sides into proportional segments.
EX 1:
Side

Splitting Converse Theorem:
If a line intersects
and
in O
distinct points X and Y so that
, then
.
X
Y
(If you know the sides are in proportion, then the line is
parallel to the base.)
P
Q
EX 2:
is a segment which splits two sides of
as shown. Is
?
EX 3: In
below,
. Find x, LM, ON.
EX 4: Given TO = 6 meters, OP =
4 m, TR = 7.2 m, RE = 4.8 m.
(a) Are
and
parallel? Why / why not?
(b) If PE = 12 m, what is OR (the length of the support)?
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