Chapter 10.2, Problem 17WE

To determine

To construct: A parallelogram with an angle of degree $n$ and sides of lengths a and b.

Explanation of Solution

Given information: The figures,

  

Construction:

  

  

Interpretation:

At first, a straight line is drawn, then a point is chosen on the straight line and is labelled as R. The compass is set for radius a. Using R as the center, an arc is drawn intersecting the line. The point of intersection is labelled as S Thus, a straight-line RS is constructed having a length of a.

Using B as the center and any radius, an arc intersecting BA and BC is drawn. The points of intersection are labelled as D and E. Again, using R as the center and the same radius, an arc is drawn intersecting RS at Y. Using Y as the center and radius equal to DE, an arc is drawn intersecting the previous arc at X. RX is drawn and is extended in the upward direction. Thus, $\angle XRY=n°$ .

Similarly, using S as the center and the same radius, an arc is drawn intersecting RS at V. Using V as the center and radius equal to DE, an arc is drawn intersecting the previous arc at U. SU is drawn and extended upward. Thus, $\angle USV=n°$ .

Now, the compass is set for radius b. Using R as the center, an arc is drawn intersecting the line RX. The point of intersection is labelled as P. Again, using S as the center, an arc is drawn intersecting the line SU. The point of intersection is labelled as Q. Then, PQ is drawn.

Hence, a parallelogram PQRS is constructed with an angle of $n°$ and sides having lengths of a and b units.