Question

State ‘true’ or ‘false’:
The diagonals of a parallelogram bisect each other at right angle:-
a) True
b) False

Answer 1

Hint:- Before solving this question, let us know about angle bisectors.
ANGLE BISECTOR: A line that splits an angle into two equal angles is called an angle bisector.
(To ‘bisect’ means to divide into two equal parts)
Let us now learn about Parallelogram.
PARALLELOGRAM: A parallelogram is a four – sided, 2 – dimensional figure which has opposite sides parallel.
Let us now learn about the properties of a parallelogram.
Here are some of the important properties of a parallelogram:-
1) If one angle of a parallelogram is a right angle, then all angles of it are right.
2) The diagonals of a parallelogram bisect each other.
3) Each diagonal of a parallelogram separates it into two congruent.

Complete step-by-step answer:
So now,
As mentioned in the hint provided above, we can see that one of the properties of a parallelogram is that the diagonals of a parallelogram bisect each other.
We can observe that “bisect each other at 90°” is not mentioned in the properties. And it is a fact that the diagonals of a parallelogram bisect each other, but do not make an angle of 90°.
So, the statement is not true. It is false.
Note:- Let us now know about the other three properties of a parallelogram:-
1) Opposite sides of a parallelogram are congruent.
2) Opposite angles of a parallelogram are congruent.
3) Consecutive angles of a parallelogram are supplementary.