Question

In the figure OA = OB and OD = OC. Show that (1)Triangle AOD is congruent to Triangle BOC (2)AD is parallel to BC

Answer 1

(1) Given :

OA = OB

And OD = OC

To Prove:

ΔAOD ≅ ΔBOC

Proof :

Lines CD and AB intersect.

∠AOD = ∠BOC   (Vertically Opposite Angles)

In ΔAOD and ΔBOC,

  OA = OB   (Given)

  ∠AOD = ∠BOC    (Vertically Opposite Angles)

    OD = OC    (Given)

Therefore, ΔAOD ≅ ΔBOC    (By SAS Congruence)----- (1)

(2) To prove:

  AD ║ BC

Proof :

Since ΔAOD ≅ ΔBOC   {From  (1)}

    ∠OAD = ∠OBC    { CPCT }

 ∠OAD  and ∠OBC for the pair of Alternate angles.

If a transversal intersects two lines such that the pair of Alternate interiors Angles are equal, then the Lines are Parallel.

 Therefore, AD ║ BC .

Answer 2

Answer:

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