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Similar Triangles I Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT © 2002 East Los Angeles College. All rights reserved. Click one of the buttons below or press the enter key

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In geometry, two polygons are similar when one is a replica (scale model) of the other. EXIT BACKNEXT

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Consider Dr. Evil and Mini Me from Mike Meyers’ hit movie Austin Powers. Mini Me is supposed to be an exact replica of Dr. Evil. EXIT BACKNEXT

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Triangles are a class of polygons in geometry. Therefore we can talk about triangles that are similar. The following is a picture of similar triangles. EXIT BACKNEXT

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Note: One triangle is a scale model of the other triangle. EXIT BACKNEXT

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Q: How do we truly know that the above two triangles are similar (scaled model)? EXIT BACKNEXT

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Answer– We must take a closer look at the sides of our triangles. The following conditions must all be satisfied. EXIT BACKNEXT

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Scaling Factor EXIT BACKNEXT

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This can all be summarized as: Scaling factor EXIT BACKNEXT

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Our problem becomes as follows: Scaling factor This tells us that ABC and XYZ are similar. EXIT BACKNEXT

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Q: Can these triangles be similar? EXIT BACKNEXT

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Answer—Yes, right triangles can also be similar but use the criteria. EXIT BACKNEXT

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This tells us our triangles are not similar. You can’t have two different scaling factors! Do we have equality? EXIT BACKNEXT

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Q: The two triangles below are known to be similar, determine the missing value X. EXIT BACKNEXT

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Answer– Using the fact that our triangles are similar... The missing side has a length that’s 3 units. The picture should look like this... EXIT BACKNEXT

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Q: The following triangles are similar. Can you determine the missing sides X and Y? EXIT BACKNEXT

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Answer– Using the criteria, EXIT BACKNEXT

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Our triangles should look like this: EXIT BACKNEXT

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Let’s take a closer look at the criteria that tells us when triangles are similar: EXIT BACKNEXT

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Mathematicians find this next relationship useful as well. Why? EXIT BACKNEXT

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End of Similar Triangles I Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA Phone: (323) Us At: Our Website: EXIT BACKNEXT

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