Question

the diagonals of a parallelogram bisect each other​

Answer 1

Answer:

Now, we have to tell if the diagonals of a parallelogram bisect each other at right angles or not.

For this, we will take a parallelogram and try to find if it is true or not.

Now, let ABCD be a parallelogram with diagonals AC and BD intersecting at point O.

Now, we will first find if the diagonals bisect each other or not.

Now, let us take ΔAOD and ΔCOB.

In ΔAOD and ΔCOB,

AD=BC (opposite sides of a parallelogram are equal)

∠AOC=∠COB (vertically opposite angles)

∠ADO=∠CBO (alternate interior angles of a parallelogram)

Thus, ΔAOD≅ΔCOB (AAS)

Hence, OD=OB and AO=CO by CPCT.

Thus, the diagonals of a parallelogram bisect each other.

Now, for the diagonals to bisect each other at right angles, i.e. for ∠AOD=∠COB=90∘, the sum of the other two interior angles in both the triangles should be equal to 90∘.

But this may or may not be true because only the opposite angles are in the parallelogram are true which may or may not be equal to 90∘.

Hence, the diagonals of a parallelogram bisect each other but not necessarily at right angles.

Thus, the given statement is false.

Hence, option (B) is the correct answer.

Note: There are some parallelograms whose diagonals bisect each other at right angles. These are namely, rectangle, square, and a rhombus. A square is a parallelogram with all interior angles as right angles, a square is a rectangle with all the 4 sides equal and a rhombus is a parallelogram with all sides equal.

Answer 2

Answer:

The diagonals of a parallelogram bisect each other at right angles. ... For this, we will take a parallelogram ABCD with diagonals AC and BD intersecting each other at point O. Then, we will take any two opposite triangles out of the 4 triangles in the parallelogram formed by the intersection of the 2 diagonals.