13-3 The Side-Splitting Theorem

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10 Οκτ 2013 (πριν από 4 χρόνια και 28 μέρες)

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13
-
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)?