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Which construction is shown in the figure below? A- - B C

Which construction is shown in the figure below? A- - B C

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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### Geometric Construction Assessment **Question:** Which construction is shown in the figure below? **Figure Description:** The figure consists of a horizontal line segment labeled \( AB \) with endpoints \( A \) and \( B \). There is a vertical line segment labeled \( DF \) intersecting \( AB \) at point \( C \), forming right angles at the intersection. Two arcs are drawn from points \( D \) and \( F \), such that each arc passes through point \( C \) and meets the other arc above and below the line \( AB \). **Answer Choices:** A. Copy of line segment \( AB \) B. Copy of line segment \( DF \) C. Perpendicular bisector of line segment \( AB \) D. Perpendicular bisector of line segment \( DF \) The correct answer is: **C. Perpendicular bisector of line segment \( AB \)** **Explanation:** The construction shown in the figure is that of the perpendicular bisector of line segment \( AB \). This is determined by the vertical line \( DF \), which cuts the horizontal line segment \( AB \) exactly at point \( C \), its midpoint, forming right angles (90 degrees) with \( AB \). The arcs intersecting above and below point \( C \) further confirm that \( DF \) is the perpendicular bisector.
Transcribed Image Text:### Geometric Construction Assessment **Question:** Which construction is shown in the figure below? **Figure Description:** The figure consists of a horizontal line segment labeled \( AB \) with endpoints \( A \) and \( B \). There is a vertical line segment labeled \( DF \) intersecting \( AB \) at point \( C \), forming right angles at the intersection. Two arcs are drawn from points \( D \) and \( F \), such that each arc passes through point \( C \) and meets the other arc above and below the line \( AB \). **Answer Choices:** A. Copy of line segment \( AB \) B. Copy of line segment \( DF \) C. Perpendicular bisector of line segment \( AB \) D. Perpendicular bisector of line segment \( DF \) The correct answer is: **C. Perpendicular bisector of line segment \( AB \)** **Explanation:** The construction shown in the figure is that of the perpendicular bisector of line segment \( AB \). This is determined by the vertical line \( DF \), which cuts the horizontal line segment \( AB \) exactly at point \( C \), its midpoint, forming right angles (90 degrees) with \( AB \). The arcs intersecting above and below point \( C \) further confirm that \( DF \) is the perpendicular bisector.
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