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. ​

Answer 1

Answer:

In rhombusa

all side are equal and diagonols are different but intersect at 90

⇒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

Answer 2

Answer:

Here is the answer

Step-by-step explanation:

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