ABCD is a rhombus. Show that diagonal AC bisects angle A as well as angle and diagonal BD bisects angle B as well as angle D
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AB=BC=CD=DA⇒AC⊥BDInΔABC⇒AB=BC⇒∴∠CAB=∠ACB⇒AO=OC∴∠ABO=∠CBOandsimillarlyinΔADC⇒AD=DC⇒AO=OC∴correspondingangleareequal⇒∠DAC=∠DCAand∠CDO=∠ADOHence,ACbisect∠Aand∠CandBDbisects∠Band∠D
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