Question

If in the given figure, O is the mid-point of AB and CD, prove that
AC = BD and AC || BD.
[Hint: Prove triangle OAC congruent triangle OBD by SAS congruence criterion]​

Answer 1

Answer:

In triangles AOC and BOD, we have

AO = BO (O, the midpoint of AB);

∠AOC=∠BOD, (vertically opposite angles);

CO=OD, (O, the midpoint of CD)

So by SAS postulate we have

△AOC≅△BOD.

Hence, AC = BD, as they are corresponding parts of congruent triangles.

solution