Problem
GEO-B2-M01-P001 One Chord in Oriented Notation
#1
★★☆☆☆ Level 2 of 5
Points \(A,B,C,D\) lie on one circle. Prove that \(\angle ABC\equiv\angle ADC\pmod{180^\circ}\).
Both angles stand on chord \(AC\). Think about what changes when \(B\) and \(D\) lie on opposite sides of \(AC\).
If points \(B\) and \(D\) lie on the same side of chord \(AC\), then \(\angle ABC\) and \(\angle ADC\) are equal as inscribed angles standing on the same chord. If they lie on opposite sides, the angles are supplementary. In both cases the oriented notation gives \(\angle ABC\equiv\angle ADC\pmod{180^\circ}\).
The basic transition from ordinary circle geometry to oriented angles.