Question

ABCD is a rhombus. Show that AC bisects angle A as well as angle c and bd bisects angle b as well as angle d​

Answer 1

Answer:

rhombusallsideareequalanddiagonolsaredifferentbutintersectat90

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⇒AB=BC=CD=DA

⇒AC⊥BD

InΔABC

⇒AB=BC

⇒∴∠CAB=∠ACB

⇒AO=OC

∴∠ABO=∠CBO

andsimillarlyinΔADC

⇒AD=DC

⇒AO=OC

∴correspondingangleareequal

⇒∠DAC=∠DCA

and∠CDO=∠ADO

Hence,ACbisect∠Aand∠CandBDbisects∠Band∠D

solution