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Geometric Exploration: Triangles, Polygons, Perimeters, and Areas

Delve into the world of geometry by exploring triangles named by angles and sides, measuring angles in polygons, informal proof of polygon angle sums, identifying quadrilaterals, pinpointing properties, calculating perimeter and area in geometric shapes, analyzing bumper cars with constant area, investigating wreck-tangles with constant perimeter, and experimenting with triangle side lengths. Develop informal proofs for interior angles of polygons and discover patterns in angle measurements. Compare shapes with equal areas but different perimeters and vice versa. Explore designing bumper car rides based on area and perimeter constraints. Investigate how the areas of rectangles with equal perimeters differ. Engage in practical activities using materials like push pins, string loops, and cardboard. Draw conclusions about geometric concepts.

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Geometric Exploration: Triangles, Polygons, Perimeters, and Areas

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  1. Math Institute Geometry and Measurement August 17, 2004 Exploring Triangles (naming by angle and by side) Measuring Angles in Polygons Informal Proof: Sum of the Angles in Polygons Quadrilaterals Quad Nets Pinpointing Properties Perimeter and Area Bumper-Cars (constant area) Wreck Tangles (constant perimeter)

  2. Can a triangle be made with three sides of any length?

  3. Draw a conclusion about the lengths of the sides of a triangle.

  4. Angles in Polygons

  5. Developing an Informal Proof for the Sum of Interior Angles of Polygons Use the geoboards to make different polygons. Divide the polygon into triangles. Measure the angles. Find a pattern.

  6. What can you say about the number of sides of a polygon and the sum of its interior angles?

  7. Perimeter and Area Is it possible for two shapes to have the same area but different perimeters? Explain your answer by using words and drawings. Is it possible for two shapes to have the same perimeter but different areas? Explain your answer by using words and drawings. Can you figure out a perimeter if you know its area? Why or why not?

  8. Designing Bumper-Car Rides Each tile represents one square meter. A bumper car ride design that consists of only one square meter would require 4 meters of bumper rail to surround it. How many meters of railing are needed for this floor plan? Begin a table for recording data.

  9. Designing Bumper-Car Rides Begin a table for recording data.

  10. Designing Bumper-Car Rides Design a bumper-car floor plan with an area of 24 square meters and a perimeter of 22 meters. Design a bumper-car floor plan with an area of 24 square meters and many rail sections. What is the floor plan with the most rails? With the fewest number of rails?

  11. Wreck-Tangles How do areas of rectangles with equal perimeters compare? Complete this activity using the push pins, 30 cm string loop, cardboard and worksheet. Conclusion:

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