2.7.4 Practice: Modeling: Similarity Theorems
Geometry Sem 1
Practice
Name:
Date:
YOUR ASSIGNMENT: About Face!
Your Peak of Choice
Your friend Tyler is preparing to climb a rock face and wants to figure out how far he will
need to climb to reach one of three different peaks. You remember a trick you can use to help
him out. You realize that if you place a small mirror on the ground and move it to where
Tyler can see the reflection of the peak in the mirror, then the angles from the mirror to Tyler
and from the mirror to the peak are congruent.
Use what you have learned about triangles, the mirror, Tyler, and the peak to find the height
of the peak.
Defining Your Triangles
1. Which peak did you select? (1 point)
Tyler will climb peak __________.
2. In the drawing below, label the distances given for the peak you chose. (3 points: 1 point
for each correct distance)
3. According to the information given, what can you determine about the triangles formed by
Tyler, the mirror, and the peak? How do you know the relationship between the two
triangles? (4 points: 2 points for correctly describing the triangles, 2 points for the
explanation)
4. To find the height of the peak, list the corresponding sides and angles of the two triangles
you and Tyler have created. (6 points: 1 point for each pair of sides or angles)
Finding the Height
5. Which segment of the triangle will give you the height of your peak? Write the equation
for the proportion that will allow you to find the height. (2 points: 1 point for identifying the
correct segment, 1 point for the correct equation)
6. Use your equation to find how high Tyler will have to climb to scale the peak. (4 points: 2
points for correctly substituting values, 2 points for the correct height)
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2.7.4 Practice: Modeling: Similarity Theorems