This document provides instruction on using proportions to solve for missing parts of triangles. It introduces the side-splitter theorem, stating that a line parallel to one side of a triangle divides the other two sides proportionally. It also covers the parallel line theorem about corresponding and alternate interior angles being equal, and the triangle-angle-bisector theorem about the bisector dividing the opposite side proportionally. Examples demonstrate using these theorems to find unknown side lengths or angle measures. Students are assigned practice problems from their workbook and textbook.

1. 7.5: Proportions in
Triangles
Objective: Use the "side-splitter"
theorem and triangle angle bisector
theorem to find missing parts of
triangles.
Standard: Geometry 4.0 (similarity) and
Geometry 7.0 (parallel lines)

2. Ex. 1) Find the value of x.
7
5 x
12

3. The Side-Splitter Theorem:
If a line is __________ to one side of a
triangle and intersects the two other
sides, then it divides those sides
_____________
=
c
a
d
b

4. Ex. 2) Find the value of x.
a) x b)
6
9
x+4
12 10 12
2x

5. Bonus Parallel Line Theorem
If three parallel lines intersect two
transversals, then the segments intercepted
on the transversals are _____________
a c
=
b d

6. Ex. 3) Solve for x and y.
6 5
x 12.5
9 y

7. Triangle-Angle-Bisector Theorem
If a ray _______ an angle of a triangle,
then it divides the _________ side into
two segments __________ to the other
two sides.
a b =
c d

8. Ex. 4) Find the value of x.
5
6 8
x

9. Assignments:
#4 7.5 Worksheet
(workbook p. 387)
#5 Textbook p. 390
#1-24 (all)
[Read examples on the
page first!]