Question

Prove that diagonal AC of rhombus ABCD bisecys angle A as well as angle C
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Answer 1

Answer:

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