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Present the following discovery activity as a
group activity, class demonstration, enrichment project, extra credit,
etc.
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Task: Using a
mean proportional, prove the Pythagorean Theorem which
states: "The sum of the squares of the lengths of the legs
of a right triangle equals the square of the length of the
hypotenuse."
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Steps:
1. Prepare a drawing of a right triangle. Draw (or
construct) the altitude to the hypotenuse. Label the
lengths of the segments for the sides of the original triangle
and the segments of the hypotenuse.
2. Using your knowledge of mean
proportionals in relation to right triangles, establish
proportions relating the segments.
3. Using your proportions, prove the
Pythagorean Theorem. This may be done in paragraph form or
in a two-column format. |
Solution:
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Using the Leg
Rule for the leg labeled "a", we know:
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Using the Leg
Rule for the leg labeled "b", we know:
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a proportion, the product of the means equals the product of
the extremes. |
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Equal quantities may be added
to equal quantities.
The distributive property.
The whole is equal to the sum
of its parts (d + e = c in the
drawing).
Substitution. |
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