Math Adventures
Parallel Lines Challenge
Teacher’s Guide
Welcome to the Math Adventures Parallel Lines Challenge! I hope that you and your students
will enjoy this challenge and will learn through the process.
Website address: https://www.mathadventures.net/parallel-lines-challenge
Access Password: none (this adventure is free)
Mathematical Concepts:
This adventure was designed to take place after students have explored parallel lines and
transversals. Students will have to use critical thinking skills to solve puzzles related to parallel
lines along with some additional ones that are just designed to build thinking skills.
This adventure addresses the following High School Common Core Mathematics Standards:
G.CO.12. Make formal geometric constructions with a variety of tools and methods (compass
and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a
line parallel to a given line through a point not on the line.
G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that
passes through a given point).
Story:
The notorious criminal, Fran Kersal, has hidden an explosive device in her yard. It is up to you to
find and deactivate this device before it explodes.
Toolkit:
Below is information you will need through your quest.
Fran Kersal's cronies use the monikers "L", "M", "N", "O", and "P". Look for these terms in the
team's communications.
Detectives have broken a secret code that Fran Kersal and her cronies use to communicate.
Alternate Exterior Angles = 0
Alternate Interior Angles = 1
Complementary Angles = 2
Corresponding Angles = 3
Linear Pair = 4
Same Side Exterior Angles = 5
Same Side Interior Angles = 6
Vertical Angles = 7
Key:
Challenge #1
You must begin by finding the location of Fran's house. Police have gathered photographic
evidence which indicates that her home is located at an intersection with an angle of 105 degrees.
Below is a map of her neighborhood. Find Fran's address and use this number to unlock the next
clue.
Answer:
Use the triangle with address #3944 to help find some of the unknown angles; #3944 is 108˚ by
alternate exterior angles, and the bottom right angle is 61˚ by vertical angles. Using these angles,
the bottom left angle is 11˚.
This angle allows you to solve the triangle with address #6097. The right angle is 11˚ by vertical
angles, and the bottom left angle is 64˚ by corresponding angles. This means that address #6097
is 105˚ and is Fran Kersal’s home.
Challenge #2
You come up to the front door and see a four-digit keypad and the following image. Find the
code to get you into her home.
Answer:
Use the toolkit code to find numbers that align with the different types of angles. The red are
corresponding, which is #3. The yellow, alternate interior, is code #1. Green are alternate
exterior, code #0, and then finally blue are also corresponding, which is code #3 again.
#3103 is the code that will open the door.
Challenge #3:
A search of the house does not turn up the explosive. The house is well organized without much
clutter. Inside the study is a safe with a six letter lock (all capital letters from A-Z).
There is a single piece of paper located in the desk drawer which may have clues for opening the
safe:
Oldest → Youngest
I am the oldest!
All of my partners are born in 1979, except O was born in 1973 and M was born in 1984.
Each of us has our birthdays in a different month.
N’s birthday is in March.
L’s birthday is not in a winter month.
P’s birthday occurs on Thanksgiving some years.
Answer:
Fran is the oldest, her last name, Kersal, gives the code of K (many students use I, watch for
this).
1973 is older than 1979, so O is next.
Someone born earlier in the year is older than someone born later in the year. P is born in
November, N in March, and L is not born in January, February, or December. This means that L
must be between N and P, since no one has the same birthday month.
Final code: KONLPM
Challenge #4:
In the safe is a map. Use this map to find the coordinates of the hidden explosive.
Each unit on the map is one meter.
To find the hidden location, you must walk parallel to the path.
As you walk you must directly pass the rock.
The hidden location is 7 meters to the east of the house.
Give the coordinate north (the y coordinate), in the form y.y (for example, 2.3).
Answer:
6
The path has a slope of 5, so you must walk at the same slope to form a parallel line.
This new trail must pass directly by the rock at (5, 3). We can use algebra to find the y-intercept
of this trail:
3=
6
(5) + 𝑏
5
3= 6+𝑏
−3 = 𝑏
6
So our new trail has an equation: 𝑦 = 5 𝑥 − 3
The x-coordinate of the treasure is 7, plug in to find the coordinate north:
𝑦=
6
42
(7) − 3 =
− 3 = 𝟓. 𝟒
5
5
Challenge #5:
You find the explosive device after carefully digging at the point 7 meters east and 5.4 meters
north of the house. Now you must deactivate it before it detonates.
Your detective team tells you that they have found that you must transcribe an image on the
cover of the device to deactivate it. The image is given below. The image must be transcribed
perfectly onto the outer cover to keep the device from detonating. The angles K and P must be
the perfect measurement.
Give the measurements of the two angles as a four-digit number in the form KKPP.
Answer: 4657