Similar Definition

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Similar is comparison between two given quantities. In math similarity is used in various topics. In geometry similar term is used for two geometric objects with the same shape. For a given geometric object the other geometric object is obtained by scaling (i.e. enlarging or shrinking), translating, reflecting or rotating. This means that one of the geometric object can be obtained by un-scaling, reflecting or rotating the other geometric figure. This implies that all the circles are similar to each other. All the equilateral triangles are similar to each other. All the squares are similar to each other.  

 
Example 1: Find if the given two triangles are similar to each other and why?


Solution: Given is two triangles with different geometric measurements.
Comparing the side lengths of both the triangles.
This gives, 6 / 3 = 8 / 4 = 5 / 2.5 = 2
This proves that the ratio of the side lengths for both the given triangles is same.
This means that the corresponding sides of both the triangles are similar.
Hence they are similar triangles.


Example 2: Find if the given two triangles are similar to each other and why?


Solution: Given is two triangles with different geometric measurements.
Comparing the side lengths of both the triangles.
This gives, 9 / 3 = 3; 8 / 4 = 2.
This proves that the ratio of the side lengths for both the given triangles are not the same.
This means that the corresponding sides of both the triangles are not similar.
Hence they are not similar triangles.
 

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