Question

A point O is taken inside a rhombus ABCD such that OB = OD. Prove that the points A, O and C are collinear points.​

Answer 1

Answer:

In ΔAOD and ΔAOB

AB=AD      ...[Given]

AO=AO      ...[Common]

OD=OB      ...[Given]

So, ΔAOD≅ΔAOB      ...[SSS congruence criterion]

Also, ∠AOD=∠AOB    ...[CPCT]    ...(1)

Similarly,  ΔDOC≅ΔBOC      ...[SSS congruence criterion]

⟹∠DOC=∠BOC     ...[CPCT]   ...(2)

But ∠AOB+∠AOD+∠COD+∠BOC=3600    ...[Point angle]

⇒2∠AOD+2∠COD=3600     ...[Using (1) and (2)]

⇒∠AOD+∠COD=1800

So, ∠AOD and ∠COD form linear pair.

⇒Ao and OC are in the same straight line.

⇒AOC is a straight line

Answer 2

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