Problem
GEO-B1-M04-P002 Equal Opposite Sides
#2
★☆☆☆☆ Level 1 of 5
In parallelogram \(ABCD\), prove that \(AB=CD\) and \(BC=AD\).
Draw diagonal \(AC\) and prove two triangles congruent.
Draw \(AC\). From \(AB\parallel CD\), \(\angle BAC=\angle ACD\); from \(AD\parallel BC\), \(\angle BCA=\angle CAD\). Side \(AC\) is common. Thus \(\triangle ABC\cong\triangle CDA\) by a side and two adjacent angles. Therefore \(AB=CD\) and \(BC=AD\).
Connects the triangle congruence module with quadrilaterals.