Street Sign Production
Signs are everywhere, in many forms: traffic control signs, street signs, and work zone
signs, to name a few. Have you ever thought about the detail and precision that goes
into designing and producing an effective sign? In what ways would a minor
measurement error affect the outcome? In this task, you will explore angle relationships
using a variety of shapes and sizes.
As you work through the task, think about these questions: How can you use known
angle measures to find unknown angle measures? How are similar figures used to
make scale drawings?
Directions:
Complete each of the following tasks, reading the directions carefully as you go. You will
need a piece of blank paper and a piece of graph paper for this task.
You will be graded on the work you show, or your solution process, in addition to your
answers. Make sure to show all of your work and to answer each question as you
complete the task. You will be given partial credit based on the work you show and the
completeness and accuracy of your explanations.
Now let’s get started!
Step 1: Angle relationships and congruence
a) You are riding your bike and notice the square sign above. You mentally draw a
straight line from point A to C. Describe the angle relationship between ∠DCA and
∠BCA. (2 points)
b) Your sister says that the angles ∠DCA and ∠BCA are supplementary angles. Is she
correct? Explain your reasoning. (1 point)
c) Is triangle DCA congruent to triangle BCA? Explain. (2 points)
Step 2: The third-angle theorem
a) Drivers of semi-trucks and other large vehicles pay close attention to signs similar to
the one below. These signs indicate a change in the grade or slope of the road. Look
at the black scalene triangle in the sign. How can the third-angle theorem be applied
to find all three angle measurements in the black triangle? (2 points)
b) Are the black triangle and orange triangle above congruent or similar? Explain. (1
point)
Step 3: Two parallel lines cut by a transversal
For our safety, it is important that drivers recognize a stop sign immediately. Stop signs
are made with exact side and angle measurements to form a regular octagon. They are
red so they are easy to see. The three lines drawn below are straight lines. Lines a and
b are parallel.
a) The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the
angle measure for ∠L? Describe the relationship between ∠F and ∠L. (1 point)
b) What is the measure of ∠E? Explain how you know. (1 point)
c) Describe the relationship between ∠E and ∠K. What is the measure of ∠K? (1 point)
d) What is the measure of ∠H? Explain. (1 point)
e) What is the measure of ∠I? Explain. (1 point)
f) Describe the relationship between ∠H and ∠L. (1 point)
Step 4: Sum of interior and exterior angles
a) Suppose you are a designer making the traffic sign above. What is the sum of the
interior angles of the equilateral triangle? What is the measure of ∠N? What is the
measure of ∠M? Explain your reasoning. (2 points)
b) What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X?
Explain your reasoning. (2 points)
Step 5: Similar figures, slope, and the equation of a line
a) Imagine that you need to create a scale drawing of this sign. The scale drawing
will be used to create a mold that will be used to manufacture the sign. Use the grid
to make a scale drawing of this sign. Include a key to show the relationship
between the dimensions in the scale drawing and the dimensions of the actual sign.
Label all sides in the scale drawing. Show your work. (3 points)
b) Draw a vertical y-axis on the left-hand side of your graph and label it. Then draw
a horizontal
x-axis at the bottom of your graph. Then label the coordinates of each corner of the
sign on your graph. Draw line a on your graph. What is the slope of line a? [2 points]
c) What is the equation of line a? [2 points]