“Is it better to be feared or respected? And I
say, is it too much to ask for both?”
7.5:
Proportions
in Triangles
Side-Splitter Theorem
Theorem 7-4: 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.
Side-Splitter Proof
Given : QXY with RS || XY
XR YS
Prove :

RQ SQ
Statements
Reasons
1. RS || XY
1.
2. 1  3, 2  4
2.
3. QXY ~ QRS
4. XQ  YQ
RQ SQ
3.
5. XQ  XR  RQ, YQ  YS  SQ
5.
6. XR  RQ  YS  SQ
RQ
SQ
7. XR  YS
RQ SQ
6.
4.
7.
Side-Splitter Theorem
Find the value of x.
Find the value of x.
Corollary to Side-Splitter Theorem
Corollary to Theorem 7-4: If three parallel lines intersect two
transversals, then the segments intercepted on the transversals are
proportional.
a c
b


d
Application
Given that the edges of the panels of the sails are parallel, find the
values of the variables.
You wanna try one? Too bad! ;)
Find the values of the variables in the following figure.
Triangle-Angle-Bisector Theorem
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.
Triangle-Angle-Bisector Theorem
Find the value of x in the following figure.
Find the value of x in the following figure.
Kick it up a notch!!!
Find the value of x.
Kick it up a notch!!!
Find the value of x.
“Don’t worry Wilson, I’ll do all the
paddling. You just hang on!”
7.5 Proportions in Triangles
HW 7.5: #1-7, 8-24 even, 25, 27, 31-33