## Construct a parallelogram with two adjacent sides 3cm and 5.6cm and one angle as 105°. pls guys it’s very urgent.​

Question

Construct a parallelogram with two adjacent sides 3cm and 5.6cm and one angle as 105°.

pls guys it’s very urgent.​

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3 weeks 2021-11-07T08:36:47+00:00 1 Answer 0 views 0

How do I construct a parallelogram when only given two adjacent sides?

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If you have two adjacent sides, I think that we have to assume that you are given not only the length of each of them, but also their relationship to each other. This means that you have a V-shaped figure with sides of certain lengths which are attached at one point forming an angle of a certain size.

If you are given the lengths of these sides and the angle between them, you can easily construct a parallelogram from the “V” shape with Euclid’s tools of straight edge and compass, with resorting to coordinates on a Cartesian plane.

You must know what a parallelogram is: It is a four-sided planar figure whose opposite sides are parallel. Of course, we could take time to prove that this requires that the lengths of the opposite sides are equal, but let’s just take it for granted.

To construct the parallelogram asked for in the question, carefully draw the given part of the diagram. For this part, if you are drawing it from a given figure or a description, you can depart from Euclid a little and measure each side and the angle between them with appropriate measuring devices.

Once you have the given “V”, put a compass point at the end of one leg of the “V” and draw an arc whose radius is equal to the length of that leg. The repeat this procedure with the other leg. Make sure that you draw the arcs in such locations that they intersect out beyond the open part of the original “V”. Now draw a line from each of the open ends of the “V” to the intersection of the arcs. Each of these lines will be the same length as and parallel to one of the legs of the original “V”.

The resulting figure will be the parallelogram you have been asked to find.