Question

7. 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.

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Answer 1

Answer:

AC bisects ∠A and ∠C and BD bisects ∠B and ∠D

Step-by-step explanation:

[In rhombus all side are equal and diagonals are different but intersect at 90°]

⇒AB=BC=CD=DA

⇒AC⊥BD

In ΔABC

⇒AB=BC

⇒∴∠CAB=∠ACB

⇒AO=OC

∴∠ABO=∠CBO

and similarly in ΔADC

⇒AD=DC

⇒AO=OC

∴the corresponding angle is equal

⇒∠DAC=∠DCA and ∠CDO=∠ADO

Hence, AC bisects ∠A and ∠C and BD bisects ∠B and ∠D