Proving Similar Triangles Name: _______________________________Partner Activity

1. Height of a lamppost example:

A. Guess how tall the lamppost is.

B. Draw two similar triangles depicting the scenario below and explain why we know that the two triangles are similar.

C. What information or tools would help you find a better estimate as to the exact height of the lamppost? Check with Ms. Urquhart for this information.

Low Guess High Guess Actual Guess

D. Use the fact that the triangles are proportional to find a more exact height of the lamppost?

E. Check with Ms. Urquhart and record what the actual height of the lamppost.

F. After the exact answer was provided, how close was your original guess (From part A)?

G. How close were you in your calculation (From part D)? Why might your calculation be a little off?

2. Radiation therapy example:(Note this is a vintage machine – There are updated medical machines available now)

A. Watch the intro video provided by Ms. Urquhart. Draw two similar triangles depicting the scenario below and explain why we know that the two triangles are similar.

B. Where did the length 100cm come from? How about the 5 cm? Are these fixed or variable lengths?

C. Use the fact that the two triangles are proportional to find the exact length of the spinal cord getting hit with radiation in the video? (Just the base of the larger triangle)

D. Watch the video provided by Ms. Urquhart to find the answer to the question:“How much of the spine in centimeters is getting hit with radiation?”

(Just the base of the larger triangle)

E. What the video fails to mention is the entire horizontal length of the spine getting hit with radiation? This is shown in red. Find the entire length of the red line shown below.

F. Sequel: Let say a shorter person, then the man in the video, needs to receive radiation therapy.

If segment C need to be 48 cm long, how far apart do the two vertical lines need to be set (i.e. segment A)?

What would the length of segment B need to be marked on that person back?

Can you draw a sketch of how you might mark up someone’s back to prevent overlapping rays.

A

BC

3. Mirror Trick Example:

A. Watch the intro video provided by Ms. Urquhart. Draw two similar triangles depicting the scenario below and explain why we know that the two triangles are similar.

B. What quick calculation did the teacher put in her calculator to approximate the Brad’s height within an inch?

C. What is the Brad’s height in the video?

D. Check your answer to part A and part C with Ms. Urquhart.

How close was your answer? Why might it have been a little off?

From watching the solution video, finish the sentence:

The famous principle in physics is that the angle of ? is equal to the angle of ? . What does this principle mean?

E. Try this trick out with your partner. See how well it works for you. Record your data and finding below.

F. Sequel: Let try this trick in reverse with you and Peter Dinklage.

Let say you had to setup this trick, but in reverse, where you would place the mirror on the floor and require that each person stand a set distance away, so that the surprise would be that you would see the top Peter Dinklage. Moreover, if the angle of incidence equals the angle of reflection you did you calculation correctly.

How would you set it up? What information do you need? How far from the mirror would you need to stand from the

mirror? How far from the mirror would Peter Dinklage need to stand?

4. Pool/Billiards Application:

A. Watch: https://www.youtube.com/watch?v=3gLNUV8wgOE

B. Be ready to discuss this in class at a later date. Jot down any notes you have below.