Problem
GEO-B1-M02-P012 A Quadrilateral with Equal Opposite Sides
#12
★★☆☆☆ Level 2 of 5
In quadrilateral \(ABCD\), it is known that \(AB=CD\) and \(BC=AD\). Prove that \(\angle ABC=\angle CDA\).
Draw diagonal \(AC\).
Consider triangles \(ABC\) and \(CDA\). They have \(AB=CD\), \(BC=AD\), and common side \(AC\). By SSS, the triangles are congruent. Therefore the corresponding angles \(ABC\) and \(CDA\) are equal.
The auxiliary diagonal is an important simple tool.