2.7.4 Practice: Modeling: Similarity Theorems
Geometry Sem 1 (S2758702)
Points possible: 20
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: 2 points 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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