Remark 2: Euclid's proof amounts to solving the above equation. Construct the square ABCD, given segment AB. Let E be the midpoint of AD. Construct the point of intersection, F, of the dircde centered at E of radius EB and the extension of segments DA, as shown. Now construct square AFGX, all of whose sides have length AF, with X on segment AB.Claim: X is the desired point.Notice that A E = 1 2 A D = 1 2 a(ii)Apply the Pythagorean Theorem to the right triangle ABE to find EB in terms of a.EB=______

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Remark 2: Euclid&#039;s proof amounts to solving the above equation. Construct the square ABCD, given segment AB. Let E be the midpoint of AD. Construct the point of intersection, F, of the dircde centered at E of radius EB and the extension of segments DA, as shown. Now construct square AFGX, all of whose sides have length AF, with X on segment AB.Claim: X is the desired point.Notice that   A  E  =      1    2    A  D  =      1    2    a(ii)Apply the Pythagorean Theorem to the right triangle ABE to find EB in terms of a.EB=______

Payton Mcbride · Accepted Answer

In triangle ABE, AB and AE are perpendicular sides while EB is the hypotenuse.AB = a and AE = 0.5aApplying Pythagoran&#039;s Theorem, we have :  E      B    2    =  A      E    2    +  A      B    2    &amp;lt;  b  r  &amp;gt;  E      B    2    =  (  0.5  a      )    2    +      a    2  Hence, EB = 1.12a

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