Question

ABCD is a rhombus show that diagonal AC bisects angle A as well as angle C and diagonal BD bisects Angle B as well as angle D.
please answers this question in full explaination.​

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]

so, ∆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.