Question

In a rhombus ABCD show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.


Don't spam ​

Answer 1

= In the rhombus all sides are equal

⇒AB=BC=CD=DA

⇒AC⊥BD

In ΔABC

⇒AB=BC

⇒∴∠CAB=∠ACB

⇒AO=OC

∴∠ABO=∠CBO

and simillarly inΔADC

⇒AD=DC

⇒AO=OC

∴corresponding angle are equal.

⇒∠DAC=∠DCA

and∠CDO=∠ADO

Hence,ACbisect ∠Aand∠C and BDbisects ∠Band ∠D

$MARK AS BRAINLIEST☑️$

Answer 2

$\huge\pink{αɳรωεɾ}$

= In the rhombus all sides are equal

⇒AB=BC=CD=DA

⇒AC⊥BD

In ΔABC

⇒AB=BC

⇒∴∠CAB=∠ACB

⇒AO=OC

∴∠ABO=∠CBO

and simillarly inΔADC

⇒AD=DC

⇒AO=OC

∴corresponding angle are equal.

⇒∠DAC=∠DCA

and∠CDO=∠ADO

Hence,ACbisect ∠Aand∠C and BDbisects ∠Band ∠D