Mathematics
In the given figure, BC // DA and BC = DA, then :
AB and CD bisect each other
AB ≠ CD
OA = OC
OA = OD
Answer
In △ BOC and △ DOA,
⇒ ∠DOA = ∠BOC (Vertically opposite angles are equal)
⇒ ∠OAD = ∠OBC (Alternate angles are equal)
⇒ ∠ODA = ∠OCB (Alternate angles are equal)
∴ △ BOC ≅ △ DOA (By A.A.A. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ OD = OC and OA = OB.
∴ AB and CD bisect each other.
Hence, Option 1 is the correct option.
Related Questions
Which of the following is true for the given figure :
△ ABD ≅ △ ACD
angle BAD ≠ angle CAD
△ ABD ≇ △ ACD
∠EAB = ∠BAD
In the given figure, ∠x = ∠y and PO = RO, then :
RB = AO
BO = PA
BP = AR
RB = OB
The following figure shows a circle with center O. If OP is perpendicular to AB, prove that AP = BP.
In a triangle ABC, D is mid-point of BC; AD is produced upto E, so that DE = AD. Prove that :
(i) △ ABD and △ ECD are congruent.
(ii) AB = EC
(iii) AB is parallel to EC.