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Quadrilateral WXYZ is similar to quadrilateral QRST. Which segment corresponds to YZ? S. T Y z, R Q

Quadrilateral WXYZ is similar to quadrilateral QRST. Which segment corresponds to YZ? S. T Y z, R Q

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Geometry Question 17: Corresponding Segments in Similar Quadrilaterals #### Problem Statement: Quadrilateral WXYZ is similar to quadrilateral QRST. Which segment corresponds to \(\overline{YZ}\)? #### Diagram Analysis: The problem contains two quadrilaterals: - Quadrilateral WXYZ with vertices labeled in sequence as W, X, Y, and Z - Quadrilateral QRST with vertices labeled in sequence as R, Q, S, and T The two quadrilaterals are shown with their shapes and relative proportions indicating that they are similar. #### Answer Choices: - A. \(\overline{QR}\) - B. \(\overline{QT}\) - C. \(\overline{ST}\) - D. \(\overline{RS}\) In this problem, you need to determine which side of quadrilateral QRST corresponds to side \(\overline{YZ}\) of quadrilateral WXYZ, based on the understanding of the similarity of shapes. #### Explanation: When two quadrilaterals are similar, corresponding angles are equal and corresponding sides are proportional. In this case, the corresponding vertices should match in order. - \(W \leftrightarrow R\) - \(X \leftrightarrow Q\) - \(Y \leftrightarrow S\) - \(Z \leftrightarrow T\) Therefore, the side \(\overline{YZ}\) in quadrilateral WXYZ corresponds to the side \(\overline{ST}\) in quadrilateral QRST. #### Correct Answer: - C. \(\overline{ST}\) Understanding this correspondence is essential for solving problems related to similarity in geometric shapes. It requires recognizing the pattern of corresponding parts and applying the properties that define similarity in polygons.
Transcribed Image Text:### Geometry Question 17: Corresponding Segments in Similar Quadrilaterals #### Problem Statement: Quadrilateral WXYZ is similar to quadrilateral QRST. Which segment corresponds to \(\overline{YZ}\)? #### Diagram Analysis: The problem contains two quadrilaterals: - Quadrilateral WXYZ with vertices labeled in sequence as W, X, Y, and Z - Quadrilateral QRST with vertices labeled in sequence as R, Q, S, and T The two quadrilaterals are shown with their shapes and relative proportions indicating that they are similar. #### Answer Choices: - A. \(\overline{QR}\) - B. \(\overline{QT}\) - C. \(\overline{ST}\) - D. \(\overline{RS}\) In this problem, you need to determine which side of quadrilateral QRST corresponds to side \(\overline{YZ}\) of quadrilateral WXYZ, based on the understanding of the similarity of shapes. #### Explanation: When two quadrilaterals are similar, corresponding angles are equal and corresponding sides are proportional. In this case, the corresponding vertices should match in order. - \(W \leftrightarrow R\) - \(X \leftrightarrow Q\) - \(Y \leftrightarrow S\) - \(Z \leftrightarrow T\) Therefore, the side \(\overline{YZ}\) in quadrilateral WXYZ corresponds to the side \(\overline{ST}\) in quadrilateral QRST. #### Correct Answer: - C. \(\overline{ST}\) Understanding this correspondence is essential for solving problems related to similarity in geometric shapes. It requires recognizing the pattern of corresponding parts and applying the properties that define similarity in polygons.
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