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Similar Triangles

Similar Triangles. Click one of the buttons below or press the enter key. BACK. NEXT. EXIT. In geometry, two polygons are similar when one is a replica (scale model) of the other. BACK. NEXT. EXIT.

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Similar Triangles

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  1. Similar Triangles Click one of the buttons below or press the enter key BACK NEXT EXIT

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

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

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

  7. 1. 2. 3. Scaling Factor BACK NEXT EXIT

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

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

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

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

  12. BACK NEXT EXIT

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

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

  15. 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

  16. BACK NEXT EXIT

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

  18. Answer– Using the criteria, BACK NEXT EXIT

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

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

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

  22. 12 16 9 12

  23. Compare the ratio of any two corresponding sides in simplest form. 16/12 = 4/3

  24. Find the Perimeters of each rectangle and express their ratio in simplest form. 56/42 = 4/3

  25. Find the Areas of each rectangle and express their ratio in simplest form. 192/108 = 16/9

  26. Make an observation about the relationship among the three simplified ratios. • Corresponding sides…..4/3 • Perimeters……………..4/3 • Areas…………………..16/9 The ratio of the perimeters is equal to the ratio of the corresponding sides. The ratio of the areas is equal to the square of the ratio of the corresponding sides.

  27. End of Similar TrianglesClasswork/Homework BACK NEXT EXIT

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