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Some random thoughts on this unit: I think it is valuable to the students because the rest of the semester they will be able to refer back to these constructions for properties and proofs. Additionaly, they will aquaire a good understanding of terminology as well as the ability to visualize and work through problems.
This unit is meant to be very engaging and also informative- not just instructional. Students should come away from the unit thinking not about how 'stupid' or unrelevant the math problems are but that they didn't realize there was so much geometry in the world around them.
More eloquent words on the subject:
Why are geometric constructions important for geometry students and teachers? "Trying to learn geometry without using geometric construction is like trying to learn chemistry or biology without using laboratories. Basic knowledge and skills on geometric constructions help students to discover and explore geometric relationships and interpret geometric concepts and theorems. They can also help the teachers to transform the static and confusing array of definitions and theorems typically found in geometry textbooks into an active and exploratory investigation of geometric relationships. Computer-based geometric construction programs such as Geometers Sketchpad enable both students and teachers to explore geometric relationships dynamically and to create very complex and yet very precise geometric constructions and diagrams.
As any mathematics teacher knows, and as most students soon come to realize, geometric figures are nearly always helpful for the analysis and solution of real world problems and for learning new mathematical ideas. Although the geometric constructions as we have defined them are not, strictly speaking, necessary for such graphical descriptions of problems or ideas, their precision can often reveal aspects of the problem or idea that may not be evident in an informal paper or blackboard sketch. Teachers usually find that extra time spent in producing excellent graphical reprentations and figures for class handouts and exams is rewarded by better student understanding and interpretation of problems and ideas."