1. Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a line and A, C are on opposite sides of the line BD. The lengths of the line segments AB, BC, CD and DA are 4, 3, 6 and 8 respectively. (a) What is the range of possible values for the length of the line segment BD? You should justify your answer carefully! (b) Now suppose that x = 7. What is the length of the line segment AC?

1. Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a line and A, C are on opposite sides of the line BD. The lengths of the line segments AB, BC, CD and DA are 4, 3, 6 and 8 respectively. (a) What is the range of possible values for the length of the line segment BD? You should justify your answer carefully! (b) Now suppose that x = 7. What is the length of the line segment AC?

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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Question

1. Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them
lie on a line and A, C are on opposite sides of the line BD. The lengths of the line
segments AB, BC, CD and DA are 4, 3, 6 and 8 respectively.
(a) What is the range of possible values for the length x of the line segment BD? You
should justify your answer carefully!
(b) Now suppose that x = 7. What is the length of the line segment AC?

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why did you use 1,2,3,4 in the answer when the lengths are 4,3,6,8 ?

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