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SAS Criteria for Congruency

In the given ...

Question

In the given figure, if AB = BC = CD = DA, OD = OB, then ∠DOC is equal to

∠AOB

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∠AOD

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∠BOC

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∠OBC

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Solution

The correct option is C ∠BOC
In ΔDOC and ΔBOC.
DC = BC (Given)
OD = OB (Given)
OC = OC (Common)
∴ ΔDOC ≅ ΔBOC (SSS congruence rule)
⇒ ∠DOC = ∠BOC (CPCT)
Hence, the correct answer is option (c).

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Similar questions

A C

B D

A B C D

O

O B = O D

A B = C D

a r (D O C) = a r (A O B)

a r (D C B) = a r (A C B)

D A ∥ C B

A B C D

In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:

(i) ar (DOC) = ar (AOB)

(ii) ar (DCB) = ar (ACB)

(iii) DA || CB or ABCD is a parallelogram.

[Hint: From D and B, draw perpendiculars to AC.]

O B = O C a n d A O + O C = 10 c m, t h e n (O D + O B)

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