2nd blank: Rectangle because Opposite angles are equal, and so each angle intercepts the same amount of arc. Between the two of them, they intercept the entire circle, so each intercepts half a circle of arc, or 180° (or π radians). Recall that the measure of an inscribed angle is equal to half the intercepted arc. Therefore, each of the opposite angles is 90° (or π/2 radians). This must also be true for the other pair of opposite angles, so the parallelogram has four right angles; thus, it is a rectangle.

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Apr 7th, 2015

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