draw a triangle abc in which ab=5 cm bc=6 cm and angle abc= 60 degrees

construct another triangle similar to triangle abc with scale factor 5/7 { 5 upon 7 }

Answer  :

We follow these steps to construct angle ABC   .

Step 1 :  Draw a line BC = 6 cm  .

Step 2 :  Now take any radius ( Less than half of BC ) and take center  " B "  draw an arc that intersect our line BC at  " P " , With same radius and center is " P "  draw another arc that intersect our previous  arc at "  Q " .

Step 3 :    Join BQ and extend it to D

Step 4 :  Take radius = 5 cm and center "  B "  we draw an arcs that intersect our line BD at "  A "  Now we join AC , and get triangle ABC .

Now We construct another triangle with scale factor $\frac{5}{7}$ , As :
              
Step 5 : Draw a line BX  As  $\angle$ CBX is any acute angle and draw seven equal radius arc on line BX that intersect at X₁ . X₂ , X₃ , X₄ , X₅ , X₆ and  X₇ AS :

  BX₁  = X₁ X₂ = X₂ X₃ = X₃X₄ = X₄X₅ = X₅X₆ = X₆ X₇

Step 6 : Join X₇ to C and than draw a line from X₅  as parallel to X₇C that intersect our line BC at C' .

Step 7 : Draw line from C' as parallel to AC that intersect line AB at A'  .



We get triangle A'BC' whose sides are $\frac{5}{7}$ of corresponding sides of triangle ABC .