Question

the diagonals of a parallelogram ABCD intersect at o. A line through O intersects AB at X and DC at Y prove that OX=OY​

Answer 1

Answer:

⇒  In given figure ABCD is a parallelogram.

∴    AB∥DC

⇒  Also AC is a transversal of AB∥DC.

∴  ∠1=∠2             [Alternate interior angles]

⇒  Now in △AXO and △CYO, we have

⇒  ∠1=∠2         [Alternate interior angles]

⇒   ∠3=∠4       [Vertically opposite angles]

⇒  CO=OA            [Diagonals bisect each other]

∴    △AXO≅△CYO      [ASA Criteria]

∴   OX=OY      [CPCT]

Step-by-step explanation:

Answer 2

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⇒ In given figure ABCD is a parallelogram.

∴ AB∥DC

⇒ Also AC is a transversal of AB∥DC.

∴ ∠1=∠2 [Alternate interior angles]

⇒ Now in △AXO and △CYO, we have

⇒ ∠1=∠2 [Alternate interior angles]

⇒ ∠3=∠4 [Vertically opposite angles]

⇒ CO=OA [Diagonals bisect each other]

∴ △AXO≅△CYO [ASA Criteria]

∴ OX=OY [CPCT]