Question

D 9. In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at O. A line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF. A E ​

Answer 1

$\huge \fbox \blue{♡ANSWER:}$

Given:

In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at O. A line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF. A E

A.T.Q:

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

$\fbox {Consider \: ∆AOE \: and \: ∆COF}$

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)