Divide a straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part. (i) Let AB be the given straight line. It is required to divide it internally in K, so that AK2 = AB BK. On AB describe square ACDB. Bisect AC in E. Join EB and produce CA to G making EGEB. On AG describe square AGHK, then K is the required point. Produce HK to L [Fig. 59 (i)]. G H K' A B K B A E D E C G D

Divide a straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part. (i) Let AB be the given straight line. It is required to divide it internally in K, so that AK2 = AB BK. On AB describe square ACDB. Bisect AC in E. Join EB and produce CA to G making EGEB. On AG describe square AGHK, then K is the required point. Produce HK to L [Fig. 59 (i)]. G H K' A B K B A E D E C G D

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter2: Parallel Lines

Section2.4: The Angles Of A Triangle

Problem 5E: Describe the auxiliary line segment as determined, overdetermined, or underdetermined. a Draw the...

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