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.


We draw a quadrilateral ABCD  and also similar quadrilateral to AB'C'D' with scale factor 45 , As :
Step 1 :  Draw any quadrilateral ABCD .
Step 2 : Join AC . Below AC, draw a line AX  As  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  45 of the corresponding sides.                (Ans)

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