Triangle Similarity Theorems Activity: Fix it Felix!

Armed with your knowledge about similar triangles and the theorems associated with it, you are now ready to do the following task.

The Situation:

Suppose that you are a car mechanic. Your job is to fix your customer's car so they can safely drive around the city. One day, one customer enters your shop to have his car repaired.
You take a quick look at the car and you notice that it has some parts that needs repairing! You quickly open your toolbox and start repairing. The tools below are what you are going to use to fix your customers car.

You will use triangle similarity theorems to accomplish your task.

You will use triangle similarity theorems to accomplish your task.
SAS - Side-Angle-Side theorem AA - Angle-Angle theorem SSS - Side-Side-Side theorem


You will repair the customer's car part-by-part by accomplishing the tasks. You will use the appropriate tools (triangle similarity theorems) in order to successfully finish the tasks below.

Task # 1

You first look at the engine at the front. You find out that you need to replace one of the parts. To replace this, the replacement part should be similar to the broken part.
Under the hood, you see the following objects:

Which among the three parts is similar to the triangle on the left?

Which tool are you going to use to fix this part? Explain how this theorem is applicable in this problem.

Task #2

After fixing the first part, you look at the second portion of the car. You notice that the transmission needs some tweaking. Your task is to adjust the bolts on the right to make it similar with the main bolt at the left.
Below the midsection of the car, you see the following:
(Use the red points to manipulate the bolts)

What did you consider to make the bolts similar to the main bolt? What are the measurements of the sides opposite to the angles highlighted in green after adjusting the bolts?

Which tool did you use to fix the problem? What did you observe after manipulating the parts?

Task #3

Finally, you check the rear part of the car for damages. You see that one of the brake lights are broken. You intend to 'install' the new brake light onto the slot to finish up the repairs. Your task is to compare a set of triangles and determine which brake lights are viable for installation.
You zoom in closer on the slot where the brake light is supposed to go and you see the following:
Drag the red triangles only. Do not drag the blue points. Make sure that the blue points are on the green triangle.

Observe all the triangles and compare the brake lights with the slot by dragging it over the slot. What can be inferred about measure angle X, Y, and Z? What can be inferred about their adjacent sides? Using this reasoning, which brake lights are similar to the slot?

Which tool did you use in solving this problem? How did this theorem apply on this specific problem?

After fixing all the parts, you give the car back to your customer. It's now time to enjoy your break and relax your eyes from continuously squinting! Maybe buy some ice scream with the customer's payment.
What are your conclusions after this activity? Make sure to explain the similarity theorems that you have applied throughout the activity. Summarize your learnings in bullet points. Write your learnings on a sheet of paper and submit it to your teacher.