According to fundamental operations of plane geometry, a plane figure can be moved from one point o another point (called Translation), can be rotated about the fixed point (called Rotation) or can be expanded or contracted such that the distance between the points in the plane figure increases or decreases in the same ratio (called Expansion). IF any figure is subjected to any of these operations in succession will result to similar figure or one figure can be brought to coincide with another by using the above properties. We have noticed similar figures like the map of the world or country, model of a house or a dam, in all these cases the similar figures bear a constant ratio with the original. In this section let us discuss about the similarity and few problems based on similar figures.

## Similarity Definition

Similarity Definition: Two figures are similar, if they have the same figures. Similar figures differ in size.

The following diagrams show pairs of similar figures.

Uses of similarity: Similarity is very much useful to make models of buildings, roads, factory etc. We have seen that maps which show the geographical location of the place. We easily find the distance between any two places in the word using the scale factor shown in the map. The housing plan also help us to construct buildings.

Similar Triangle: Two triangles are said to be similar if they are equiangular and the corresponding sides are proportional.

The following diagram shows the pair of triangles which are similar and the corresponding proportional sides.

Similarity Ratio: In the above two triangles, $\Delta ABC$ and $\Delta PQR$,
$\angle A$ = $\angle P$
$\angle B$ = $\angle Q$
$\angle C$ = $\angle R$

$\frac{BC}{QR}$ = $\frac{AC}{PR}$ = $\frac{AB}{PQ}$, this ratio is called Similarity Ratio.

1. If two triangles are equiangular then their sides opposite to equal angles are proportional.
2. If the sides of two triangles are proportional, then the angles opposite to proportional sides are equal

### Surface

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