Honors Geometry Section 8.4
The Side-Splitting Theorem
We can use similar triangles to find the measures
below. Why is  A E B ~  A D C ?
AA
35
AC = _____
28
ED = _____
3
70
3
AD = _____
23 . 4
BE = _____
The Side-Splitting gives us another way of find
some of the lengths from the previous problem.
Side-Splitting Theorem
A line parallel to one side of a triangle
will DIVIDE THE OTHER TWO SIDES
PROPORTIONALLY
One obvious proportion resulting
from this theorem would be
ET

TA
EC
CH
but others that are useful are
ET

EA
or……..
or
EA
TA

Example: Consider the
figure on the right.
1) TA = 6
AX = 10
TE = 8
TS = ______
2) TA = 5
TX = 14
ES = 12
TE = __________
3) TA = 8
AX = 12
TS = 30
TE = _____
4) TA = 5
AX = 8
AE = 3
XS = ____
The following statement is a corollary of the
Side-Splitting Theorem.
Two-Transversal Proportionality
Corollary
Three or more parallel lines will
divide two transversals
proportionally.
Examples: Complete each
proportion.