Zachary is given △ABC, and is instructed to construct a median of the triangle. Zachary places his compass at C and draws two arcs on either side of AB¯¯¯¯¯¯¯¯. He then maintains the compass width and places the needle of the compass on A, drawing two more arcs intersecting the previously drawn arcs. He draws a line through the point of intersection to find D, the midpoint of AB¯¯¯¯¯¯¯¯. Zachary then draws CD¯¯¯¯¯¯¯¯ and declares that the median has been constructed. Is Zachary's construction accurate? Explain

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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Zachary is given △ABC, and is instructed to construct a median of the triangle. Zachary places his compass at C and draws two arcs on either side of AB¯¯¯¯¯¯¯¯. He then maintains the compass width and places the needle of the compass on A, drawing two more arcs intersecting the previously drawn arcs. He draws a line through the point of intersection to find D, the midpoint of AB¯¯¯¯¯¯¯¯. Zachary then draws CD¯¯¯¯¯¯¯¯ and declares that the median has been constructed. Is Zachary's construction accurate? Explain.

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