Bisection of Angle/Construction

Bisection of Angle: Construction

Let $\angle BAC$ be the given angle to be bisected.

Let $D$ be an arbitrary point on $AB$.

From Proposition $3$: Construction of Equal Straight Lines from Unequal, let $AE$ be cut off from $AC$ such that $AE = AD$.

From Euclid's First Postulate, let the line segment $DE$ be constructed.

From Proposition $1$: Construction of Equilateral Triangle, let an equilateral triangle $\triangle DEF$ be constructed on $AB$.

From Euclid's First Postulate, let the line segment $AF$ be constructed.

Then the angle $\angle BAC$ has been bisected by the straight line segment $AF$.

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 1 (2nd ed.) ... (previous) ... (next): Book $\text{I}$. Propositions