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?

Options

• 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.

• 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.

• With one of the vertices as center 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.

• None of these helps in constructing a similar parallelogram.

Answer 1

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.

Explanation:-

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 center 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.