Prove that the diagonals of the rhombus bisect the interior angles.

Question

anonymous · Answer

attachment

campbell_st · Answer

prove congruency in triangles ABC and ADC

triangle ABC                 Triangle ADC

               AB                       AD     ( sides in a rhombus are equal)
               BC                       DC      (sides in a rhombus are equal)
                          AC                       (common side)

therefore triangles ABC and ADC are congruent by Side, Side Side test. 

Angle BAC = Angle DAC   (corresponding angles in congruent triangles)
Angle BCA =  Angle DCA  (corresponding angles in congruent triangles)

therefore AC bisects angles BAD and BCD 

same style of proof for triangles BAD and BCD