Mathematical_Recreations-Kraitchik-2e

Geometric Recreations 197
SoZ1dion: Let the pentagon be ABCDE (Figure 73). Cut
off the triangle CDE along CE and place it beside the piece
ABCE so that C falls on A, and D on B. DE will then form
the continuation EF of CE, so that ABCF A is a trapezoid
equivalent to the pentagon. Through the mid point G of AF
draw a parallel to BC meeting CF at K, and BA produced
o
F
...... - - --- - - - - -r -~---r'--'----->"---'----~ C
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I
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I
I I
FIGURE 73. A Pentagon Dissected to Form an Equivalent Square.
at I. IBCK is then a parallelogram equivalent to the trapezoid
and to the pentagon, and it may be formed by cutting
along GK and placing the triangle FGK with F at A, K at I
and G at G. From I as center draw an arc of a circle with
radius equal to the mean proportional between the base I B
and corresponding altitude of the parallelogram, and let the
arc cut CK at L. Draw IL, and through B draw a perpendicular
to IL meeting IL at M. When the parallelogram has