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The image shows a dilation of an equilateral triangle by scale
factors of 1, 2, 3, and 4. At each stage, the dilated shape is
partitioned into triangles congruent to the original.
1. Why is the difference in the number of original triangles that
fit into the image between 2 successive scale factors always
odd?
2. What does this image tell us about the sum of the first n odd
numbers?