7.5
Proportions in
Triangles
Side Splitter Theorem
Corollary to the Side Splitter
Triangle-Angle-Bisector Theorem
Side-Splitter Theorem
If a line is parallel to one side of a triangle
and intersects the other two sides, then it
divides those sides proportionally.
Q
XR YS

RQ SQ
R
X
S
Y
#1 Using the Side-Splitter Theorem

Find the value of x.
x  1 .5
5

x
2 .5
2.5(x + 1.5) = 5x
2.5x + 3.75 = 5x
3.75 = 2.5x
1.5 = x
x + 1.5
x
5
2.5
Corollary to the Side-Splitter Theorem

If three parallel lines intersect two
transversals, then the segments intercepted
on the transversals are proportional.
a c

b d
c
a
b
d
#2 Using the Side-Splitter Theorem

Solve for x and y.
16.5 15

y
26
x 15

30 26
y
16.5
15
x
15 y  429
26x  450
y  28.6
x  17.3
26
30
Triangle-Angle Bisector Theorem

If a ray bisects an angle of a triangle, then it
divides the opposite side into two segments
that are proportional to the other two sides of
the triangle.
B
D
AC AD

CB DB
A
C
#3 Using the Triangle-AngleBisector Theorem

Find the value of y.
5 3.6

8
y
5 y  8(3.6)
5 y  28.8
y  5.76
3.6
5
y
8
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7.5 Practice
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