Category 2: 4 sides, 4 right angles Category 5: 4 sides, all the same length Category 3: 4 sides, 4 right angles, opposite sides parallel Category 6: 4 sides, all the same length, opposite sides parallel Category 8: 4 sides, opposite sides parallel Category 10: 4 sides, at least one pair parallel Category 4: 4 sides, 4 right angles, opposite sides same length Category 7: 4 sides, all the same length, opposite angles same size Category 9: 4 sides, opposite sides same length Category 12: 4 sides Category 11: 4 sides, exactly one pair parallel Which categories in part 1 have exactly the same shapes? Try to draw a shape (using a ruler and protractor or geometry software) that will fit in one of those categories but not the other. Do you think it is possible? For each category, provide its common name if you know it. Which categories are a subcategory of another category? How can you tell that from lists of properties? Describe or draw a diagram to show how the categories in part 1 are related to each other.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Category 2: 4 sides, 4 right Category 3: 4 sides, 4 right Category 4: 4 sides, 4 right
angles
angles, opposite sides
parallel
angles, opposite sides
same length
Category 5: 4 sides, all the
same length
Category 6: 4 sides, all
the same length, opposite
sides parallel
Category 8: 4 sides,
opposite sides parallel
Category 10: 4 sides,
at least one pair parallel
Category 7: 4 sides, all
the same length, opposite
angles same size
Category 9: 4 sides, opposite
sides same length
Category 11: 4 sides, exactly
one pair parallel
Category 12: 4 sides
2. Which categories in part 1 have exactly the same shapes? Try to draw a shape (using a
ruler and protractor or geometry software) that will fit in one of those categories but
not the other. Do you think it is possible?
For each category, provide its common name if you know it.
3. Which categories are a subcategory of another category? How can you tell that from
lists of pro rties? Describe or draw a diagram to show how the categories in part 1 are
related to each other.
Transcribed Image Text:Category 2: 4 sides, 4 right Category 3: 4 sides, 4 right Category 4: 4 sides, 4 right angles angles, opposite sides parallel angles, opposite sides same length Category 5: 4 sides, all the same length Category 6: 4 sides, all the same length, opposite sides parallel Category 8: 4 sides, opposite sides parallel Category 10: 4 sides, at least one pair parallel Category 7: 4 sides, all the same length, opposite angles same size Category 9: 4 sides, opposite sides same length Category 11: 4 sides, exactly one pair parallel Category 12: 4 sides 2. Which categories in part 1 have exactly the same shapes? Try to draw a shape (using a ruler and protractor or geometry software) that will fit in one of those categories but not the other. Do you think it is possible? For each category, provide its common name if you know it. 3. Which categories are a subcategory of another category? How can you tell that from lists of pro rties? Describe or draw a diagram to show how the categories in part 1 are related to each other.
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