Construct a Triangle similar to a given Traingle ABC with its Sides equal to 5/3 of the Corresponding sides of the triangle ABC. (Write the steps of construction.)

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Construct a triangle similar to a given traingle ABC with its sides equal to `5/3` of the corresponding sides of the triangle ABC. (Write the steps of construction.)







Steps of Construction:

Step 1: Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

Step 2: From B cut off 5 arcs

`"B"_1`,`"B"_2`,`"B"_3`,`"B"_4` and `"B"_5` on BX so that

`"BB"_1`, = `"B"_1``"B"_2` = `"B"_3``"B"_3` = `"B"_4``"B"_5`

Step 3: Join `"B"_3` to C and draw a line through `"B"_5` parallel to `"B"_3`C, interacting the extended line segment BC at C'.

Step 4: Draw a line through C' parallel to CA interacting the extended line segment BA at A' (see figure). Than, A' BC' is the required triangle.


Justification:

Note that △ ABC 〜 △ A'BC' (Since AC || A'C')

Therefore, `\frac{"AB"}{"A'B"}` = `\frac{"AC"}{"A'C'"}` = `\frac{"BC"}{"B'C'"}`

But = `\frac{"BC"}{"B'C'"}` = `\frac{BB_3}{BB_5}` = `\frac{3}{5}`

Therefore, `\frac{"AB"}{"A'B"}` = `\frac{"AC"}{"A'C'"}` = `\frac{"BC"}{"B'C'"}` = `\frac{3}{5}`

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