unit 3 crime scene decoders geometry: triangles

© 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.★


CSD: The eviDenCe

name:_______________________________

1.

Clue

___________ 2.

Clue

___________ 3.

Clue

___________


4.

Clue

___________ 5.

Clue

___________ 6.

Clue

___________ CrypTiC TexT meSSage

SuSpeCT

___________


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


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


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 =_______


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

____=____


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…

_______=_______


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


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


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


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

____=____


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


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


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

unit 3 crime scene decoders geometry: triangles

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