Final answer:
To construct the sum AB + 2(CD) using a straightedge and a compass, draw AB and replicate CD twice. Place CD end to end with AB and mark the new end point. A straight line from the start of AB to this point represents the sum of the lengths.
Step-by-step explanation:
Constructing a Vector Sum Using a Straightedge and Compass
To construct the sum of two lengths using a straightedge and a compass, you would firstly use the tools to create the individual lengths AB and CD. If CD needs to be doubled, you would simply replicate CD once more using the same process. Then, you would place the end of CD at the end of AB and mark the new length. This new point would be the end of the segment representing AB + 2(CD).
Adding Vectors Geometrically: To add vectors, you would draw them head to tail. In some cases, such as when working with forces, you may also need to measure the resultant angle with a protractor. However, for simply adding lengths, angles are not necessary, and a straight line connecting the start of AB to the end of the doubled CD represents AB + 2(CD).
When constructing vector differences or sums, you could also use the parallelogram method, as described in one of the provided steps, but this is primarily when direction is an important factor, which is not the case for AB + 2(CD) as it pertains merely to lengths.