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