1. Similarity of Triangles
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2. In geometry, two polygons are similar when one is a replica (scale model) of the other.
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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.
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5. The following are similar figures.II
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6. The following are non-similar figures.II
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7. Feefee the mother cat, lost her daughters, would you please help her to find her daughters. Her daughters have the similar footprint with their mother.
Feefee’s footprint
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8. Which of the following is similar to the above triangle?1.
Which of the following is similar to the above triangle? B A C
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9. Note: One triangle is a scale model of the other triangle.
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10. How do we know if two triangles are similar or proportional?
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11. Triangles are similar (~) if corresponding angles are equal and the ratios of the lengths of corresponding sides are equal.
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12. The sum of the measure of the angles of a triangle is 1800.
Interior Angles of Triangles A B C
The sum of the measure of the angles of a triangle is 1800.
Ð A + Ð B + ÐC =1800
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13. Determine whether the pair of triangles is similar. Justify your answer.
Answer: Since the corresponding angles have equal measures, the triangles are similar.
Example 6-1b

14. If the product of the extremes equals the product of the means then a proportion exists.
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15. This tells us that  ABC and  XYZ are similar and proportional.
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16. Q: Can these triangles be similar?
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17. Answer—Yes, right triangles can also be similar but use the criteria.
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19. Do we have equality?
This tells us our triangles are not similar. You can’t have two different scaling factors!
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20. If we are given that two triangles are similar or proportional what can we determine about the triangles?
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21. The two triangles below are known to be similar, determine the missing value X.
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23. In the figure, the two triangles are similar. What are c and d ?B C P Q R 10 6 c 5 4 d
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24. In the figure, the two triangles are similar. What are c and d ?B C P Q R 10 6 c 5 4 d
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25. Sometimes we need to measure a distance indirectly
Sometimes we need to measure a distance indirectly. A common method of indirect measurement is the use of similar triangles. h 6 17
102
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27. Similarity of Triangles
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