Roadkill Cafe - Triangle Congruency 5v493e

The Roadkill Cafe • You have applied for a job as a short order cook at the Roadkill Cafe in touristy Triangleville. • In order to get the job, you must demonstrate that you can prepare the triangle-shaped sandwiches for which the Roadkill Cafe is famous. • Their Menu consists of six specially shaped sandwiches.

#1 (SSS) Spicy Summer Sausage #2 (AAA) Awesome Authentic Armadillo #3 (SAS) Succulent Aromatic Skunk #4 (SSA) Super Sized Antelope #5 (ASA) Appetizing Sesame Aardvark #6 (AAS) Aunt Annie’s Swine #7 (HL) Hare & Lettuce

Interview Process • Make each of your assigned sandwiches according to the specifications: drawing and labeling the triangle on paper, and then cutting it out. • Be sure to label each sandwich with – The shortcut name of the sandwich, – The three vertex points, and – The side lengths and/or angle measures given in the specifications.

• Be sure to write your name on the back so the chef knows who to hire. • Place your sandwich on the board in the appropriate category. • The head chef will look over your sandwiches tonight.

Closing • Look at all of the triangles posted in each group. • Are all of the sandwiches of each type exactly the same? Why or why not? • Which set (or sets) of specifications do not create sandwiches that are exactly the same? • Write a complete sentence to explain to the chef why each sandwich may or may not be a good menu item. (A good menu item can be made exactly the same every time.) Use good math vocabulary in your sentence.

Sandwich Specifications • Each triangular sandwich you create must contain all of the specified information. • For any specifications not given, you may decide the length of that side or the size of that angle. • Be sure to put all of the labels inside the triangle since you are cutting them out!

#1 (SSS) Spicy Summer Sausage • Make triangle sandwich ABC with:

• AB = 6 in • BC = 5 in • AC = 4 in Hint: For this sandwich, draw AB first. Then use two rulers to measure out the other two sides.

#2 (AAA) Awesome Authentic Armadillo • Make triangle sandwich DEF with:

• m∠ D= 60o • m∠ E = 80o o • m∠ F = 40 Hint: For this sandwich, pick any side length to get started.

#3 (SAS) Succulent Aromatic Skunk • Make triangle sandwich GHI with:

• GH = 8 in o • m∠ G = 55 • GI = 6 in

#4 (SSA) Super Sized Antelope • Make triangle sandwich JKL with:

• JK = 7 in • JL = 5 in o • m∠ K = 40 Hint: For this sandwich, draw KJ. Then draw ∠ K. Use your ruler to measure out from J 5 inches to locate L.

#5

(ASA) Appetizing Sesame Aardvark

• Make triangle sandwich MNO with:

• m∠ M = 60 • MN = 8 in • m∠ N = 45o

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#6 (AAS) Aunt Annie’s Swine • Make triangle sandwich PQR with:

• m∠ P = 40o • m∠ R = 60o • PQ = 8 in Hint: What is m∠ Q?

#7 (HL) Hare and Lettuce • Make triangle sandwich STU with:

• m∠ S = 90 • ST = 4 in • TU = 5 in

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