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Similar Triangles I

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

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Similar Triangles I

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  1. Similar Triangles I Prepared by Title V Staff:Daniel Judge, InstructorKen Saita, Program SpecialistEast Los Angeles College Click one of the buttons below or press the enter key BACK NEXT EXIT © 2002 East Los Angeles College. All rights reserved.

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

  3. 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. BACK NEXT EXIT

  4. 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. BACK NEXT EXIT

  5. Note: One triangle is a scale model of the other triangle. BACK NEXT EXIT

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

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

  8. 1. 2. 3. Scaling Factor BACK NEXT EXIT

  9. This can all be summarized as: Scaling factor BACK NEXT EXIT

  10. Our problem becomes as follows: Scaling factor This tells us that  ABC and  XYZ are similar. BACK NEXT EXIT

  11. Q: Can these triangles be similar? BACK NEXT EXIT

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

  13. BACK NEXT EXIT

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

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

  16. 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 . . . BACK NEXT EXIT

  17. BACK NEXT EXIT

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

  19. Answer– Using the criteria, BACK NEXT EXIT

  20. Our triangles should look like this: BACK NEXT EXIT

  21. Let’s take a closer look at the criteria that tells us when triangles are similar: BACK NEXT EXIT

  22. Mathematicians find this next relationship useful as well. Why? BACK NEXT EXIT

  23. End of Similar Triangles ITitle V East Los Angeles College1301 Avenida Cesar ChavezMonterey Park, CA 91754Phone: (323) 265-8784Email Us At:menteprog@hotmail.comOur Website:http://www.matematicamente.org BACK NEXT EXIT

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