Math 130 - Fall 1996 - Hartshorne - Midterm

Math 130 - Fall 1996 - Hartshorne - Midterm - THU 19:00 FAX...

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Unformatted text preview: 02/15/2001 THU 19:00 FAX 6434330 MOFFITT LIBRARY 001 Mark 130 Midterm RHartshorne 10/4/1996 If ABC is any triangle, and if the perpendicular bisectors ofAB and BC meet in a point P, sho\v that the perpendicular bisector of AC also passes through P. Write a proof 3) based on Euclid's Book I only, and cite each proposition you use by number . 02/15/2001 THU 19:01 FAX 6434330 MOFFITT LIBRARY 002 2. On the given segment AB= construct a. regular pentagon having AB as one side. Label and number your steps‘ For full creditT use 25 steps or less. 02/15/2001 THU 19:01 FAX 6434330 MOFFITT LIBRARY 003 3. Let two circles touch each other at a point A. Let two lines pass through A7 meeting the circles at further points B, C, D, E1 as shown. Prove that BC is parallel to DE Give a proof based on Euclid’s Elements, and cite the results you use by book and number. 3 02/15/2001 THU 19:01 FAX 6434330 MOFFITT LIBRARY 004 4. Make a. ruler and compass construction of three circles of different radii, each one touching the other two. Label and number steps as usualj and say a few words why your construction works. Try to use as few steps as possible. ...
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