Problem
GEO-B1-M02-P005 Vertical Angles in Congruence
#5
★☆☆☆☆ Level 1 of 5
Segments \(AB\) and \(CD\) intersect at \(O\). It is known that \(AO=CO\) and \(BO=DO\). Prove that \(AB=CD\).
Consider triangles \(AOB\) and \(COD\).
Angles \(AOB\) and \(COD\) are vertical, so they are equal. Also \(AO=CO\) and \(BO=DO\). By SAS, \(\triangle AOB=\triangle COD\). Therefore the corresponding sides \(AB\) and \(CD\) are equal.
This problem connects Module 1 with the new congruent-triangle method.