9th Class Mathematics Triangles Similarly

Similarly

Category : 9th Class

*         Introduction

 

In our day to day life, we observe different types of objects. There may be difference in size but the shapes are same. In this chapter, we will study about such types of geometrical figures which resemble same specially emphasis on triangular shape.  

 

*         Similarly

 

When two geometrical shapes which resemble like but need to be equal in size is called similar figures. Let us observe the following examples:

(i) Any two line segments are always similar.

(ii) Two circles of different radius are always similar.

(iii) For rectilinear figure if all the corresponding angles of polygon are equal and the ratio of their corresponding sides are equal the they are said to be similar.

For the above two regular hexagon, they are similar if

\[\angle \text{A}=\angle \text{P}~~~~~\angle \text{B}=\angle \text{Q}\]

\[\angle \text{C}=\angle \text{R}~~~~~\angle \text{D}=\angle \text{S}\]

\[\angle \text{E}=\angle \text{T}~~~~~\angle \text{F}=\angle \text{U}\]

and

\[\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CD}{RS}=\frac{DE}{ST}=\frac{EF}{TU}=\frac{FA}{UP}\]  

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