Noah says, "I constructed 2 perpendicular bisectors of triangle ABC. That means the point where they intersect is the circumcenter!" Andre responds, "No, we still need to check the third perpendicular bisector to make sure it intersects at the same point." Do you agree with either of them? Explain or show your reasoning.
Noah says, "I constructed 2 perpendicular bisectors of triangle ABC. That means the point where they intersect is the circumcenter!" Andre responds, "No, we still need to check the third perpendicular bisector to make sure it intersects at the same point." Do you agree with either of them? Explain or show your reasoning.
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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Transcribed Image Text:Noah says, "I constructed 2 perpendicular bisectors of triangle ABC. That means the point where
they intersect is the circumcenter!" Andre responds, "No, we still need to check the third
perpendicular bisector to make sure it intersects at the same point."
Do you agree with either of them? Explain or show your reasoning.
Expert Solution
Step 1
Work done by Noah to find circumcenter is sufficient and there is no need to draw third perpendicular bisector to ensure the circumcenter.
So
We agree with Noah and not with Andre.
Center means a point and to find any point we need only two lines.
So , two lines are sufficient condition to find a point.
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