Problem
GEO-B1-M04-P004 A Diagonal of a Rhombus
#4
★☆☆☆☆ Level 1 of 5
In rhombus \(ABCD\), prove that diagonal \(AC\) bisects angles \(A\) and \(C\).
Compare triangles \(ABC\) and \(ADC\).
In a rhombus all sides are equal, so \(AB=AD\) and \(BC=CD\). Side \(AC\) is common. Hence \(\triangle ABC\cong\triangle ADC\) by SSS. Therefore \(\angle BAC=\angle CAD\) and \(\angle BCA=\angle ACD\). Diagonal \(AC\) bisects angles \(A\) and \(C\).
Reinforces the idea that properties of special quadrilaterals are often proved by triangle congruence.