Problem
GEO-B1-M04-P001 Angles of a Parallelogram
#1
★☆☆☆☆ Level 1 of 5
In parallelogram \(ABCD\), prove that \(\angle A=\angle C\) and \(\angle B=\angle D\).
Draw a diagonal and use alternate interior angles with parallel lines.
Draw diagonal \(AC\). Since \(AB\parallel CD\), we have \(\angle BAC=\angle ACD\). Since \(AD\parallel BC\), we have \(\angle DAC=\angle ACB\). Adding the equal parts gives \(\angle A=\angle C\). Similarly, drawing diagonal \(BD\) gives \(\angle B=\angle D\).
Basic training: parallelogram properties should be derived from parallelism, not from the drawing.