# 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 X

_{1}. X

_{2}, X

_{3}, X

_{4}

_{ }and X

_{5}

_{ }such that

AX

_{1}= X

_{1}X

_{2}= X

_{2}X

_{3}= X

_{3}X

_{4}

_{ }= X

_{4}X

_{5}

Step 3 : Join X

_{5}

_{ }to C and than draw a line from X

_{4}as parallel to X

_{5}C 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.

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