Last week, eighth-grade geometry students began a study of polygons and quadrilaterals using hinged mirrors, protractors, and colored paper to construct and analyze a variety of shapes. As they built regular hexagons, equilateral triangles in two different ways, and a rhombus that was not a square, students measured the angles formed by the mirror and noticed clear patterns, such as a 60° central angle for a hexagon and a 90° angle for a rhombus.
When students attempted to create a circle, they reasoned that a shape with infinitely many sides would require an angle of zero, leading to thoughtful discussion. Along the way, students made connections between reflection, congruent triangles, and perpendicular bisectors, strengthening their ability to observe patterns, explain their thinking, and build understanding through hands-on exploration.
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