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What is Similarity and geometry of shape ?

Similarity and geometry shape

Similarity: Two objects are similar if the angles one object is equal to the angles of the other and if the sides of one object are in proportion with the sides of the other. It is important to remember that the shape of both the object however remains the same.

similar geometry of shape       

Similarity is often denoted by the sign ‘~’ to represent that objects are similar.

Similarity in triangles:

If two triangles are similar, then corresponding angles of one triangle are equal to the corresponding angles of the other, and also the sides are in proportion.

Similarity and geometry shape  Similarity and geometry shape

If ∆ABC ~ ∆PQR, then:

 

      

 

Example: Given ∆ABC ~∆DEF, and AB/DE = 10/5, find AC/DF.

similar triangle

Given: AB/DE= 10/5 = 2

Since the triangles are similar, all sides are in equal proportion

So, AB/DE =AC/DF = BC/EF = 2

Example: Given ∆PQR ~∆ABC, AB=2, PQ=6 and PR= 12 then AC=?

similar triangle

 

Since they are similar, PQ/AB=PR/AC

So, 6/2 = 12/AC

3 = 12/AC -> AC = 12/3 -> AC = 4

You can also Read our other blog Properties And Attributes Of Functions

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