Math Institute Geometry and Measurement August 17, 2004 Exploring Triangles (naming by angle and by side) Measuring Angles in Polygons Informal Proof:

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Presentation transcript:

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)

Can a triangle be made with three sides of any length? abcYes or No

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

Angles in Polygons

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. Number of SidesNumber of TrianglesSum of Interior Angles

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

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? Perimeter and Area

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. Number of TilesNumber of Rails 14 2?

Designing Bumper-Car Rides Begin a table for recording data. Number of TilesNumber of Rails 14 2? 3 4 5

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?

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: