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Question

# Construction of similar polygons is similar to that of construction of similar triangles. If you are asked to construct a parallelogram similar to a given parallelogram with a given scale factor, which of the given steps will help you construct a similar parallelogram?

A
Find a point on the larger side which divides it in the ratio of the given scale factor and using the smaller side as the other parallel side to construct the parallelogram.
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B
Find two points one on the larger side and other on the smaller side using the given scale factor and use these scaled lengths to construct a similar parallelogram.
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C
With one of the vertices as centre and radius - (scale factor multiplied with the length of the larger side). Draw two arcs on the larger and smaller sides. Use these 2 points to construct the parallelogram.
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D
None of these helps in constructing a similar parallelogram.
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Solution

## The correct option is B Find two points one on the larger side and other on the smaller side using the given scale factor and use these scaled lengths to construct a similar parallelogram. The following steps will give you the information on how to construct a similar parallelogram to ABCD. Step 1: Find points E and F on longer and smaller sides respectively using the given scale factor. Step 2: Draw a line from E parallel to smaller side AD. Step 3: Taking the length of AF and E as centre cut an arc on the line parallel to AD and let this new point be G. Step 4: Join EG and FG. Step 5: AEFG is the required parallelogram. Now we have constructed the parallelogram AEFG ∼ ABCD.

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