how to bisect an angle in steps
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To bisect a given angle.
Let angle BAC be the given angle; we are required to bisect it.
To bisect an angle
Choose any point D on AB;
from AC cut off AE equal to AD; (I. 3)
draw DE, and on it construct the equilateral triangle DEF; (I. 1)
and join AF.
Then we have bisected angle BAC by the straight line AF.
For, since AE is equal to AD, (Construction)
and AF is common to triangles EAF, DAF,
the two sides EA, AF are equal to the two sides DA, AF respectively.
And the base EF is equal to the base DF; (Construction)
therefore angle DAF is equal to angle EAF. (S.S.S.)
Therefore we have bisected the given angle BAC by the straight line AF. Q.E.F.
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