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.
• 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.
• 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.
• D. None of these helps in constructing a similar parallelogram.

Answer 1

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 $\sim$ ABCD.