Show geometrically which is greater:

How would you generate more problems like this one?

Hint: Consider

For example,

Let a = 2, b = 6, c = 3, and d = 3. We have the inequality at the right.

Write 5 other inequalities such as this one that you could show geometrically.

Can you prove that

Can the proof be argued from the geometry? or will you need to exercise algebra?

If so, under what conditions would there be an equality?

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