An angle bisector divides an angle into two equal angles. A point on the internal bisector is equally distant from the two arms, where distance to an arm is measured perpendicularly. From vertex A, draw an arc meeting the arms at D and E. With the same radius at D and E, draw arcs crossing inside the angle at P, distinct from A. Join AP. The second radius need not equal the first, but it must be the same at D and E. AD=AE, DP=EP, and AP is common. Therefore ADP AEP (SSS), and the two angles at A are equal. This supplies a reason, rather than assuming the bisector from its appearance. Example Bisecting a 60 angle gives two 30 angles. If a point on the bisector is 2 cm from one arm, its perpendicular distance from the other arm is also 2 cm. Distances to the endpoints of the arms are not the relevant distances.

An angle bisector divides an angle into two equal angles. A point on the internal bisector is equally distant from the two arms, where distance to an arm is measured perpendicularly.

From vertex \(A\), draw an arc meeting the arms at \(D\) and \(E\). With the same radius at \(D\) and \(E\), draw arcs crossing inside the angle at \(P\), distinct from \(A\). Join \(AP\). The second radius need not equal the first, but it must be the same at \(D\) and \(E\).

\(AD=AE\), \(DP=EP\), and \(AP\) is common. Therefore \(\triangle ADP\equiv\triangle AEP\) (SSS), and the two angles at \(A\) are equal. This supplies a reason, rather than assuming the bisector from its appearance.

Bisecting a \(60^\circ\) angle gives two \(30^\circ\) angles. If a point on the bisector is 2 cm from one arm, its perpendicular distance from the other arm is also 2 cm. Distances to the endpoints of the arms are not the relevant distances.

Angle bisectors

Angle bisectors