In the diagram below, \(D\) is a point on segment \(\overline{CE}\) such that \(\overline{AD}\parallel\overline{BE}\) and \(A\) is not on \(\overline{BC}.\) Line segments \(\overline{AD}\) and \(\overline{BC}\)intersect at \(P.\)
Can \(\angle CAD=\angle CBE?\)
Yes, angle CAD can equal angle CBE because lines AD and BE are parallel and line segment BC is parallel to AD or BE. Since line AD is parallel to BE, angle CAD and angle ABE are corresponding angles and are congruent. Similarly, angle BDC and angle CBD are corresponding angles and are congruent. Since line AD is not parallel to BC, angle CAD can be equal to angle CBE.
