Question

show that the diagram of rhombus abcd bisecting angle c​

Answer 1

Given : ABCD is a rhombus, i.e.,  AB = BC = CD = DA.

To Prove : ∠DAC = ∠BAC, ∠BCA = ∠DCA  ∠ADB = ∠CDB, ∠ABD = ∠CBD  Proof : In ∆ABC and ∆CDA, we have  AB = AD [Sides of a rhombus]  AC = AC [Common]  BC = CD [Sides of a rhombus]  ∆ABC ≅ ∆ADC [SSS congruence]  So, ∠DAC = ∠BAC  ∠BCA = ∠DCA  Similarly, ∠ADB = ∠CDB and ∠ABD = ∠CBD.  

Hence, diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Proved.