Question

in an figure ABCD is a parallelogram whose diagonals intersect at O .A line segment EOF is drawn to meet and AB at E and DC at F. Prove that OE = OF

Answer 1

1st AB//EF//AD and we have to proof OE =OF in //gm oppo. sides of //gm are equal OBC lie on the same base and between the //BC AND EF (1)
THEN SEE AOD LIE ON THE SAME BASE AD and between the seame//EFandAD so it is prove that OE=OF

Answer 2

Answer:

$pls \: like \: my \: answer$

Step-by-step explanation:

In ∆ODF and ∆OBE,

we have:

OD = OB (Diagonals bisects each other)

∠DOF = ∠BOE (Vertically opposite angles)

∠FDO = ∠OBE (Alternate interior angles)

i.e., ∆ODF ≅ ∆OBE

∴ OF = OE (CPCT)

Hence, proved.