IM 8.9.3 Lesson: Tessellating Polygons
Your teacher will assign you one of the three triangles. Your goal is to find a tessellation of the plane with copies of the triangle.
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[/img][br][br]Can you make a tessellation of the plane with copies of the trapezoid? Explain.
Choose one of the other two quadrilaterals. Next, rotate the quadrilateral 180 degrees around the midpoint of each side. What do you notice?
Can you make a tessellation of the plane with copies of the quadrilateral from the previous problem? Explain your reasoning.
Can you tessellate the plane with copies of the pentagon? Explain. Note that the two sides making angle [math]A[/math] are congruent.[br][br][img]data:image/png;base64,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[/img]
Pause your work here. [br][br]Take one pentagon and rotate it 120 degrees clockwise about the vertex at angle [math]A[/math], and trace the new pentagon. Next, rotate the pentagon 240 degrees clockwise about the vertex at angle [math]A[/math], and trace the new pentagon.
Explain why the three pentagons make a full circle at the central vertex.
Explain why the shape that the three pentagons make is a hexagon (that is, the sides that look like they are straight really are straight).