Draw an equilateral triangle abc of side 4cm. Construct a triangle similar to it and of scale factor 3/5. Is the new triangle also an equilateral triangle?

Dear Student,

Please find below the solution to the asked query:

We follow these steps to construct angle ABC   .

Step 1 :  Draw a line BC = 4 cm  .

Step 2 :  Now take any radius of 4 cm and take center  " B " and " C " draw arcs and these arcs intersect at " A " .

Step 3 :    Join BA and CA , We get equilateral triangle ABC . 

Now We construct another triangle with scale factor 35 , As :
              
Step 4 : Draw a line BX  As  CBX is any acute angle and draw seven equal radius arc on line AX that intersect at X1 . X2 , X3 , X4 and X5 AS :

  BX1  = X1 X2 = X2 X3 = X3X4 = X4X5

Step 5 : Join X5 to C and than draw a line from X3  as parallel to X5C that intersect our line BC at C' .

Step 6 : Draw line from C' as parallel to AC that intersect line AB at A'  .



We get triangle A'BC' whose sides are 35 of corresponding sides of triangle ABC and also a equilateral triangle .

Hope this information will clear your doubts about Constructions.

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