Question

19. A point 0 is taken inside a rhombus AB
such that its distances from the vertices B and D are equal. show that AOC is a straight line

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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=360

0

...[Point angle]

⇒2∠AOD+2∠COD=360

0

...[Using (1) and (2)]

⇒∠AOD+∠COD=180

0

So, ∠AOD and ∠COD form linear pair.

⇒Ao and OC are in the same straight line.

⇒AOC is a straight line

Step-by-step explanation:

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