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**.

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

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.

If ∆ABC ~ ∆PQR, then:

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

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=?

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

So, 6/2 = 12/AC

3 = 12/AC **->** AC = 12/3 **->** **AC = 4**

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