Problem
GEO-B1-M01-P006 Parallelism from Angles
#6
★★☆☆☆ Level 2 of 5
Lines \(AC\) and \(BD\) are cut by line \(AB\). It is known that \(\angle CAB=\angle ABD\). Prove that \(AC\parallel BD\).
Determine what type of angles \(\angle CAB\) and \(\angle ABD\) are with respect to transversal \(AB\).
Angles \(\angle CAB\) and \(\angle ABD\) are alternate interior angles for lines \(AC\), \(BD\) with transversal \(AB\). They are equal by the condition. By the parallelism criterion, \(AC\parallel BD\).
This problem trains the converse direction of the parallel-line angle property.