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The standard reads, “Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.” One of the examples given on Arizona’s standards document is, “Is it possible to draw a triangle with a 90˚ angle and one leg that is 4 inches long and one leg that is 3 inches long? If so, draw one. Is there more than one such triangle?” Multiple textbooks supposedly aligned to Common Core only give examples where three angle measures or three side lengths are given. Due to the fact that there are inconsistencies, we want to verify whether the state’s example aligns to Common Core’s intent.
We also had a question about the use of the word “constructing” in this standard. Are students required to construct triangles using a compass?
I don’t think “three measures of angles or sides” means the same thing as “three measures of angles or three measures of sides.” That is, I interpret the standard as referring to six possible measures (angles or sides), any three of which may be chosen. Of course, in some cases this leads to ambiguity, such as SSA, but that is covered by the later “more than one triangle.” So, basically, I don’t think this standard is ambiguous, and I think that it allows examples such as the Arizona one. I find the publishers’ interpretations you refer to quite puzzling.
Which geometric shapes in particular should students be able to draw in 7.G.2? Is it only triangles?
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