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© 21st Century Math Projects
Unit 3: Crime Scene Decoders Geometry: Triangles
Standard Focus: Geometry and Spatial Sense Time Range : 1-3 Days
Supplies : Pencil and Paper
Topics of Focus :
- Triangle Classification
- Interior and Exterior Angles
- Triangle Congruence
- The Centers of a Triangle
This particular was mapped to the introductory triangle curriculum of most geometry
textbooks and can be used as an enrichment or review activity.
Geometry 7.G
6. Solve real-world and mathematical problems involving area, volume and
surface area of two- and three-dimensional objects composed of triangles,
quadrilaterals, polygons, cubes, and right prisms.
Geometry 8.G
7. Apply the Pythagorean Theorem to determine unknown side lengths in
right triangles in real-world and mathematical problems in two and three
dimensions.
Congruence G-
CO
10. Prove theorems about triangles. Theorems include: measures of interior
angles of a triangle sum to 180°; base angles of isosceles triangles are
congruent; the segment joining midpoints of two sides of a triangle is parallel
to the third side and half the length; the medians of a triangle meet at a
point.
Similarity, Right
Triangles, and
Trigonometry
G-
SRT
4. Prove theorems about triangles. Theorems include: a line parallel to one
side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using triangle similarity.
Expressing
Geometric
Properties with
Equations
G-
GPE
7. Use coordinates to compute perimeters of polygons and areas of triangles
and rectangles, e.g., using the distance formula.★
© 21st Century Math Projects
CSD: The eviDenCe
name:_______________________________
1.
Clue
___________ 2.
Clue
___________ 3.
Clue
___________
© 21st Century Math Projects
4.
Clue
___________ 5.
Clue
___________ 6.
Clue
___________ CrypTiC TexT meSSage
SuSpeCT
___________
© 21st Century Math Projects
Crime Scene Decoders Geometry: Triangles
Detectives,
The sun sets, the winds blow, and the international evil genius terrorist group the Mathemagicians
wreak havoc on yet another world region. It seems they are making progress in their plans to build a
world conquering device despite our best efforts to apprehend their cronies. The Caribbean is the
victim of the latest string of heists at the hands of a henchman (or henchwoman), Trip Trey Trinidad.
One thing is sure; Trip Trey Trinidad is definitely some kind of henchperson.
As usual, the Mathemagicians have left behind a trail of notes
with a cryptic text message. The text message when substituted
correctly will calculate to the Trinidad’s favorite number. So far
there are six suspects that police have questioned. It is hoped that
someone with relatively strong geometry and reasoning skills can
crack the codes that have puzzled the detectives on the case so
far.
Since you are being brought in as a specialist you have to have definitive proof in order for any arrest to
hold up in court. You need to be prepared to state your case and demonstrate your understanding of
the following skills that Trinidad is known to use in the notes.
- Triangle Classification
- Interior and Exterior Angles
- Triangle Congruence
- The Centers of a Triangle
Be sure to include:
- Other examples of the concepts
- Definitions
- Any other relevant information.
Keep in mind, the slightest miscalculation or illegible footnote could result in a not guilty verdict. Oh,
did I mention that use of a calculator might prematurely set off his world conquering device?
Good luck to you, gumshoe.
Chief Harris
© 21st Century Math Projects
Who is Trip Trey Trinidad?
Name: Manny
Occupation: Retired Soccer
Player
Favorite Number: 11
Name: Maribel
Occupation: Art Teacher
Favorite Number: -95
Name: Sydny
Occupation: FBI Agent
Favorite Number: ¼
Name: Stu
Occupation: Model
Favorite Number: 68
Name: Pete
Occupation: Musician
Favorite Number: 213
Name: Dawne
Occupation: Archivist
Favorite Number: 1,329
© 21st Century Math Projects
Scene #1 The Citadelle –- Milot, Haiti Trip Trey Trinidad broke into the famed Caribbean castle and stole the largest cannonballs from
the storage closet. How the cannonballs will factor into the world conquering device is unknown.
Hey Mon! I could get used to crime sprees in the Caribbean! Here’s your first puzzle, mon!
Which is not a possible distance for the flight from Haiti back to Cuba?
______=______
Scene #2 Ocean World Dolphin Swim –- North Coast, Dominican Republic
Investigators believe that Trip Trey Trinidad participated in a dolphin riding competition and later stole
five dolphin babies.
Ut oh. I think we have another Finding Nemo on our hands. I have a baby dolphin that can’t find
his mother! Luckily she knows some facts about her dorsal fin.
Which Dorsal Fin is My Mom s?
1. My mom’s fin is a triangle. 2. My mom’s fin is scalene.
3. My mom’s fin is not right or obtuse.
The number of the dorsal fin is equal to
the letter ‘s’ s =_______
© 21st Century Math Projects
Scene #3 Pirates of Nassau Museum -- Nassau, Bahamas
A museum curator was shocked to see his collection of plunder and treasure maps were pirated.
These pirates are 150% sure they have congruent triangles. How many of these scallywags are wrong?
Write the reason (SSS, SAS, ASA, AAS or Not Possible) on the line.
Captain Jack Sparrow
Dread Pirate Roberts Long John Silver
D is the midpoint of 𝑩𝑪.̅̅ ̅̅ ̅ I know ∆𝐴𝐷𝐵 ≅ ∆𝐴𝐷𝐶 by ______
I know ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷 by ______
I know ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹 by ______
Morgan Adams
E is the midpoint of 𝑩𝑫.̅̅ ̅̅ ̅ I know ∆𝐴𝐵𝐸 ≅ ∆𝐷𝐶𝐸 by ______
Captain Hook
I know ∆𝐴𝐵𝐶 ≅ ∆𝐸𝐷𝐶 by ______
How many pirates were
wrong?
0 b = 0
1 d = 1
2 r = 2
____=____
© 21st Century Math Projects
Scene #4 Harrison’s Cave –- Allen View, Barbados
A busted chainsaw and broken chisels scattered, Trip Trey Trinidad appears to have cut a
dozen limestone stalactites from the Caribbean’s most famous cave.
Watch out for those stalagmites
that might fall on your head. Oh
wait, are those stalactites?
Which one’s which? Whatever,
mon. Give this puzzle a try.
Solve for the missing variables
to lead to your next clue.
w + x + y + z = the letter O
= ______
Scene #5 White Sand Beaches –- Jamaica
A lifeguard discovered on her rounds that there was not a jelly fish to be found. Later she found this
note written in the sand from Trip Trey Trinidad
In the thoughtful words of the Baha Men, “Who let the dogs out?! Ruff, Ruff, Ruff. Who let the
dogs out?!” I’m pretty sure that song is better than anything Bob Marley ever wrote. Well okay…no.
I was able to track down three stars with Caribbean roots and asked them
each to draw isosceles triangle geometry problems. They were thrilled!
Which angle is the biggest? A, B or D?
The variable of the largest angle and its measure is the clue for this puzzle…
_______=_______
© 21st Century Math Projects
Scene #6 Bermuda Triangle Café and Bakery -- Bermuda
A baker opened up her shop to find out everything was gone. Investigators said that the irony
escaped her.
And for my last act, I’ll make you all disappear! I ran into a Bermuda Triangle expert who believes
all of the ships disappear in the center of the triangle, BUT it could be the Circumcenter, Incenter,
Centroid or Orthocenter. Looking at the diagram below he’s sure four of these ships will be gone.
Which ship will survive? (The letter of this ship will be equal to 9)
_______________
_______________
_______________
_______________
The surviving
ship is…
____= 9
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
Forget it, mon. U got no chance at dis. ~T3
B A + (R B) A D + O) S
© 21st Century Math Projects
Who is Trip Trey Trinidad?
Name: Manny
Occupation: Retired Soccer Player
Favorite Number: 11
Name: Maribel
Occupation: Art Teacher
Favorite Number: -95
Name: Sydny
Occupation: FBI Agent
Favorite Number: ¼
Name: Stu
Occupation: Model
Favorite Number: 68
Name: Pete
Occupation: Musician
Favorite Number: 213
Name: Dawne
Occupation: Archivist
Favorite Number: 1,329
© 21st Century Math Projects
Scene #1 The Citadelle –- Milot, Haiti Trip Trey Trinidad broke into the famed Caribbean castle and stole the largest cannonballs from the storage closet. How the cannonballs will factor into the world conquering device is unknown.
Hey Mon! I could get used to crime sprees in the Caribbean! Here’s your first puzzle, mon!
Which is not a possible distance for the flight from Haiti back to Cuba? By triangle ineq42 - 808
______=______
Scene #2 Ocean World Dolphin Swim –- North Coast, Dominican Republic
Investigators believe that Trip Trey Trinidad participated in a dolphin riding competition and later stole five dolphin babies.
Ut oh. I think we have another Finding Nemo on our hands. I have a baby dolphin that can’t find his mother! Luckily she knows some facts about her dorsal fin.
Which Dorsal Fin is My Mom’s?
1. My mom’s fin is a triangle. 2. My mom’s fin is scalene. 3. My mom’s fin is not right or obtuse.
Distance (mi) Clue
43 a = 43
243 b = 243
694 d = 694
810 r = 810
The number of the dorsal fin is equal to
the letter ‘s’ s =_______ s = 7
© 21st Century Math Projects
Scene #3 Pirates of Nassau Museum -- Nassau, Bahamas
A museum curator was shocked to see his collection of plunder and treasure maps were pirated.
These pirates are 150% sure they have congruent triangles. How many of these scallywags are wrong? Write the reason (SSS, SAS, ASA or AAS) on the line.
Captain Jack Sparrow
Dread Pirate Roberts Long John Silver
D is the midpoint of 𝑩𝑩𝑩𝑩.����� I
know ∆𝐴𝐴𝐷𝐷𝐵𝐵 ≅ ∆𝐴𝐴𝐷𝐷𝐴𝐴 by SSS
I know ∆𝐴𝐴𝐵𝐵𝐷𝐷 ≅ ∆𝐴𝐴𝐵𝐵𝐷𝐷 by DOESN”t woRK
I know ∆𝐴𝐴𝐵𝐵𝐴𝐴 ≅ ∆𝐷𝐷𝐸𝐸𝐹𝐹 by SAS
Morgan Adams
E is the midpoint of 𝑩𝑩𝑩𝑩.����� I know ∆𝐴𝐴𝐵𝐵𝐸𝐸 ≅ ∆𝐷𝐷𝐴𝐴𝐸𝐸 by AAS
Captain Hook
I know ∆𝐴𝐴𝐵𝐵𝐴𝐴 ≅ ∆𝐸𝐸𝐷𝐷𝐴𝐴 by AAS
How many pirates were wrong?
0 b = 0
1 d = 1
2 s = 2
____=____
© 21st Century Math Projects
Scene #4 Harrison’s Cave –- Allen View, Barbados
A busted chainsaw and broken chisels scattered, Trip Trey Trinidad appears to have cut a dozen limestone stalactites from the Caribbean’s most famous cave.
Watch out for those stalagmites that might fall on your head. Oh wait, are those stalactites? Which one’s which? Whatever mon. Give this puzzle a try.
Solve for the missing variables to lead to your next clue.
20 + 45 + 115 +40 = 220
w + x + y + z = the letter O
O=______ 220
Scene #5 White Sand Beaches –- Jamaica
A lifeguard discovered on her rounds that there was not a jelly fish to be found. Later she found this note written in the sand from Trip Trey Trinidad
In the thoughtful words of the Baha Men, “Who let the dogs out?! Ruff, Ruff, Ruff. Who let the dogs out?!” I’m pretty sure that song is better than anything Bob Marley ever wrote. Well okay…no.
I was able to track down three stars with Caribbean roots and asked them each to draw isosceles triangle geometry problems. They were thrilled!
Which angle is the biggest? A, B or D?
The variable of the largest angle and its measure is the clue for this puzzle…
_______=_______ A = 57.5
Shakira
Rihanna
Wyclef Jean
© 21st Century Math Projects
Scene #6 Bermuda Triangle Café and Bakery -- Bermuda
A baker opened up her shop to find out everything was gone. Investigators said that the irony escaped her.
And for my last act, I’ll make you all disappear. I ran into a Bermuda Triangle expert who believes all of the ships disappear in the center of the triangle, BUT it could be the Circumcenter, Incenter, Centroid or Orthocenter. Looking at the diagram below he’s sure four of these ships will be gone.
Which ship will survive? (The letter of this ship will be equal to 9)
Circumcenter
5
Incenter
3
Centroid
4
Orthocenter
1
The surviving ship is…
B= 9
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
Forget it, mon. U got no chance at dis. ~T3
B + A + (R ÷ B) − A − (−3D + O) ÷ S
© 21st Century Math Projects
From Puzzle 1 r = 810
From Puzzle 2 s = 7
From Puzzle 3 d = 1
From Puzzle 4 O=220
From Puzzle 5 A = 57.5
From Puzzle 6 b = 9
B + A + (R ÷ B) − A − (−3D + O) ÷ S (9) + (57.5) + (810÷9) − (57.5) − (−3(1)+220)÷ (7)
(9) + (57.5) + (90) − (57.5) − (217) ÷ (7)
(9) + (57.5) + (90) − (57.5) − 31
99 − 31 = 68