Honors Geometry Section 8.4
The Side-Splitting Theorem
We can use similar triangles to find the measures
below. Why is AEB ~ ADC?
AA
We can use similar triangles to find the measures
below. Why is AEB ~ ADC?
21 BE 14


35 39 AD
35  BE  819
BE  23.4
21  AD  490
AD  23. 3
35
AC = _____
9. 3
ED = _____
AD = 23
_____
.3
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 EC

TA CH
but others that are useful are
ET EC

EA EH
or……..
or
EA

TA
EH
CH
Example: Consider the
figure on the right.
1) TA = 6
AX = 10
TE = 8
TS = ______
21. 3
8
6
10
6
8

16 TS
2) TA = 5
TX = 14
ES = 12
2
6
TE = __________
3
5 TE

9 12
5
14
12
3) TA = 8
AX = 12
TS = 30
TE = _____
12
8 TE

20 30
8
30
12
4) TA = 5
AX = 8
AE = 3
XS = ____
7.8
5
3

13 XS
5
3
8
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.
WX
YZ
XY
WZ
YZ
xZ