# 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 $\frac{4}{5}$ , 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)

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