construct a triangle ABC in which AB=4 cm BC=5 cm AC=6 cm .now construct a triangle similar to triangle ABC such that each of its side is 2/3 of the corresponding side of triangle ABC

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Please find below the solution to the asked query:

We follow these steps to construct angle ABC   .

Step 1 :  Draw a line BC  = 5 cm and take radius of 4 cm and center " B "  draw an arc and with radius of 6 cm and center " C "  draw an arc that intersect our previous arc at  " A "  .

Step 2 : Join AB and AC , we get triangle ABC

Now We construct another triangle with scale factor $\frac{2}{3}$ , As :
              
Step 1 : Below BC,  draw a line BX  As  $\angle$ CBX is any acute angle and draw three arcs of equal radii on line BX that intersect at X₁ . X₂ and  X₃ AS :

  BX₁  = X₁ X₂ = X₂ X₃ 

Step 2 : Join X₃ to C and than draw a line from X₂  as parallel to X₃C that intersect our line BC at C' .

Step 3 : Draw line from C' as parallel to CA that intersect line AB at A'  .



We get triangle A'BC' whose sides are $\frac{2}{3}$ of corresponding sides of triangle ABC .
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