Proportions and Similar Triangles
GeometryUnit 11, Day 8
Ms. Reed
Proportions and Similar Triangles
We will be investigating ways proportional relationships in triangles
You will need: Paper Ruler Protractor Calculator
On your paper:
1. Construct a triangle, label it ABC2. Create a line parallel to AC. Call the
intersection point on AB, D and the point on BC, E.
3. Measure DB, DA, BE, and EC4. Compare the ratios of BD/DA and BE/EC
5. WHAT DO YOU NOTICE?
Conclusion If a line is parallel to one side of
the triangle and intersects the other two sides, then it divides those sides proportionally.
This is called the Side-Splitter Theorem
Example 1 Set up the proportion
x =8
x
10
5
16
Example 2 Solve for x
x = 1.5
3
x
5
2.5
On your paper:
1. Create 3 Parallel Line2. Draw 2 transversals through the
lines so it looks like this:
3. Label as shown
a
b
c
d
What do you notice? Measure a, b, c and d. Compare the relationship between
a/b and c/d. WHAT DO YOU NOTICE?
What we discovered! If 3 parallel lines intersect two
transversals, then the segments intercepted on the transversals are proportional.
Example 3
16.5y
15 25
x
30 x =18 y = 27.5
Sail Making! When making a boat sail, all
of the seams are parallel. Find the missing variables
x = 2 ft, y=2.25 ft
2ft
2ft
3ft1.5ft
1.5ft1.5ft
x y
On your paper Create a new triangle and label it ABC Measure A Bisect A by drawing an angle with
half its measure. Label the intersection point with the
CB and the bisecting line point D Compare the ratios of CD/DB and CA/BA
WHAT DID YOU NOTICE?
Conclusion 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.
This is called the Triangle-Angle-Bisector Theorem.
Example 4 Set up the proportion
x=9.6
8
5x
6S
P
R
Q