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Question

Answers

The diagonals of a parallelogram bisect each other at right angle:-

a) True

b) False

Answer
Verified

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.

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.

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.

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