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Choose ALL answers that describe the polygon \( S T U V \) if \( S T=12, T U=12 \), \( V S=12, \mathrm{~m} \angle S=\mathrm{m} \angle U \), and \( \mathrm{m} \angle T=\mathrm{m} \angle V \).

Ask by Moran Nichols. in the United States
Jan 24,2025

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Polygon \( STUV \) has three equal sides and two pairs of equal angles, making it symmetric but not a regular polygon. It may be classified as a special type of kite or another symmetric quadrilateral, depending on the length of the fourth side.

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Beyond the Answer

The properties described for the polygon \( S T U V \) indicate that it's an isosceles trapezoid. Specifically, we have two pairs of sides that are equal (i.e., \( S T = T U = 12 \) and \( V S = 12 \)), and the angles at opposite vertices are equal (\( \angle S = \angle U \) and \( \angle T = \angle V \)). This means that \( S T \) and \( U V \) are parallel bases, and the legs \( S V \) and \( T U \) are equal in length. Given these characteristics, we can be confident that polygon \( S T U V \) is indeed an isosceles trapezoid.

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