Draw any quadrilateral ABCD. Construct another quadrilateral AB'C'D' similar to the quadrilateral ABCD with each side equal to 4/5th of the corresponding side of quadrilateral ABCD. Write the steps of construction also.

 Answer:

We draw a quadrilateral ABCD  and also similar quadrilateral to AB'C'D' with scale factor $\frac{4}{5}$ , As :
Step 1 :  Draw any quadrilateral ABCD .
                
Step 2 : Join AC . Below AC, draw a line AX  As  $\angle$ CAX is any acute angle and draw five arcs of equal radii on line AX that intersect at X₁ . X₂ , X₃, X₄  and X₅  such that

   AX₁  = X₁ X₂ = X₂ X₃ = X₃X₄ = X₄X₅

Step 3 : Join X₅ to C and than draw a line from X₄  as parallel to X₅C that intersect our line AC at C' .

Step 4 : Draw line from C' as parallel to CD that intersect line AD at D' 

Step 5 : Draw line from C' as parallel to BC that intersect line AB at B' 



Now we can say that quadrilateral AB'C'D' is similar to quadrilateral ABCD as each side  $\frac{4}{5}$ of the corresponding sides.                (Ans)