Question

abcd is a parallelogram whose diagonals intersect each other at o. through o pq is drawn. prove that op=oq

Answer 1

Answer:

Step-by-step explanation:

We know that ABCD is a parallelogram whose diagonals intersect each other at O

Consider △AOE and △COF

We know that ∠CAE and ∠DCA are alternate interior angles

⟹∠CAE=∠DCA

From the figure we know that the diagonals are equal and bisect each other

⟹AO=CO

We know that ∠AOE and ∠COF are vertically opposite angles

⟹∠AOE=∠COF

By ASA congruence criterion

△AOE≅COF

⟹OE=OF (By C.P.C.T