Portfolio Item #3: Cell Phone Tower Task
Per:______
Name:_______________________
A cell service provider has been receiving complaints from customers in Southern Georgia
regarding dropped calls, spotty connections, and unreliable internet access.
The provider has determined that adding another cell tower might remedy the problem. They
have found that the region affected most is around the cities of Albany, Valdosta, and
Waycross.
However, the planning committee has not come to a consensus. Half the committee believes
the tower should be placed at one of those 3 cities and the other half believe it should be
placed somewhere between them.
Your job will be to help the committee determine where the cell tower should be placed using
geometry practices and mathematical reasoning.
Task #1. There is a map provided to you on Page 2. Just by looking at the map (go with your
gut), choose the location that you think will be best for building the tower. Explain your
thought process. WHY do you think that would make a good location? What additional
information would help you make a better decision?
In this question, I am only grading your ability to communicate your thought process and
reasoning.
Portfolio Item #3: Cell Phone Tower Task
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Task #2. Now you will apply mathematical concepts to construct the tower’s location.
- Construct the centroid (C), incenter (I), circumcenter (CC) and orthocenter (O) using the 4
triangles that represent the triangle formed by Albany, Valdosta and Waycross on page 3.
Then, use patty paper (or parchment, tissue paper, tracing paper, etc) to trace the triangles
and point of concurrency onto the actual map below.
- Clearly label the points of concurrency as (C, I, CC, O) so that Ms. Laymon can read them.
Portfolio Item #3: Cell Phone Tower Task
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Albany
Construct the Centroid
(intersection of medians)
Waycross
NOTE: You can get full credit with
just 2 medians.
Construct the 3rd median only to
check your work (they all intersect
at the Centroid)
Valdosta
Albany
Construct the Incenter
(intersection of angle bisectors)
Waycross
NOTE: You can get full credit with just
2 angle bisectors.
Construct the 3rd angle bisector only
to check your work (they all intersect
at the Incenter)
Valdosta
Construct the Circumcenter
(intersection of perpendicular
bisectors)
Albany
Waycross
NOTE: You can get full credit with just 2
perpendicular bisectors.
Construct the 3rd perpendicular bisector
only to check your work (they all
intersect at the Circumcenter)
Valdosta
Construct the Orthocenter
(intersection of altitudes)
Albany
Waycross
Valdosta
NOTE: You can get full credit with just 2
altitudes.
Construct the 3rd altitude only to check
your work (they all intersect at the
Orthocenter)
Portfolio Item #3: Cell Phone Tower Task
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Task #3. Based on your construction work from question #2 and your knowledge of cell
towers, where should the tower be placed? Defend your choice using mathematical
vocabulary, properties of triangle centers aka points of concurrency, and the situation’s
context (e.g. reading a map, using cell phone towers, etc).
Task #4: The following is an image of a cell tower. Assume that every “Step” is parallel to each
other and to the ground. Assume that each step is exactly halfway between the steps
immediately above and below it.
If Step 2 is 16ft wide, find the length of:
Step 1 = ______ft
Step 3= _______ft
Step 4 = _______ft
I
Step 5= ________ft
Step 5
H
T
S
F
A
U
M
Step 4
Step 3
Step 2
If 𝑚∠𝑇𝐴𝑈 = 85° and 𝑚∠𝑆𝐹𝑇 = 72°, find:
m∠𝑀𝐼𝑁 = _________°
m∠𝐼𝐻𝑆 = _________°
Step 1
m∠UNM = _________°
N
Portfolio Item #3: Cell Phone Tower Task
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