Suppose each matchstick has length 1 inch. Using 12 such matchsticks, form a fig

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Pythagoras' theorem

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Suppose each matchstick has length 1 inch. Using 12 such matchsticks, form a figure with area 4 square inches. 6a. In triangle ABC, draw through A a line perpendicular to BC. Choose any point M on this line. Prove: MB² - MC² = AB² - AC². 6b. In triangle ABC, suppose a point M in the plane satisfies MB² - MC² = AB² - AC². Prove that AM ⟂ BC.

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