There are triangles where the angles don't add up to 180 degrees, angles around a point that don't add up to 360 degrees and various other shapes that break the laws of geometry.
Students could try drawing the shapes and then make a poster explaining which ones are impossible to construct and why.
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Common Core: 7.G.A.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. 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.
Tags: Drawing Angles, Constructions, Using a Protractor, Measuring Lines, Triangles,