Sirisha said "Every Rectangle is a parallelogram". Do you agree with Sirisha? Give reasons.
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Answered by
36
Solution :-
Yes, I am agree with Sirisha that every rectangle is a parallelogram.
To prove this, we will have a closer look at the properties of rectangle and parallelogram.
Properties of a Rectangle -
1) A rectangle is a 4-sided polygon
2) There are 4 right angles in a rectangle which are congruent to each other.
3) There are 2 sets of opposite parallel sides in a rectangle.
4) There are 2 congruent diagonals in a rectangle.
5) There are 2 pairs of opposite congruent sides in a rectangle.
6) There are 2 mutually bisecting diagonals in a rectangle.
Properties of a Parallelogram -
1) A parallelogram is 4-sided polygon.
2) There are 2 pairs of opposite congruent sides in a parallelogram.
3) There are 2 sets of parallel sides in a parallelogram.
4) Both pairs of opposite angles are congruent in a parallelogram.
5) There are 2 mutually bisecting diagonals in a parallelogram.
So, a rectangle has all the properties that a parallelogram has.
Hence, every rectangle is a parallelogram.
Yes, I am agree with Sirisha that every rectangle is a parallelogram.
To prove this, we will have a closer look at the properties of rectangle and parallelogram.
Properties of a Rectangle -
1) A rectangle is a 4-sided polygon
2) There are 4 right angles in a rectangle which are congruent to each other.
3) There are 2 sets of opposite parallel sides in a rectangle.
4) There are 2 congruent diagonals in a rectangle.
5) There are 2 pairs of opposite congruent sides in a rectangle.
6) There are 2 mutually bisecting diagonals in a rectangle.
Properties of a Parallelogram -
1) A parallelogram is 4-sided polygon.
2) There are 2 pairs of opposite congruent sides in a parallelogram.
3) There are 2 sets of parallel sides in a parallelogram.
4) Both pairs of opposite angles are congruent in a parallelogram.
5) There are 2 mutually bisecting diagonals in a parallelogram.
So, a rectangle has all the properties that a parallelogram has.
Hence, every rectangle is a parallelogram.
Answered by
22
Its 100% true that every rectangle is a parallelogram. In order to prove this, we must understand these terms.
A parallelogram is a quadrilateral which has two pairs of equal, opposite and parallel sides. A rectangle also has the same properties but the difference is that the angles between the adjacent sides are always right angles i-e. 90°.
But in case of parallelogram, the angles are not necessarily right angles. This clearly shows that every rectangle is a parallelogram. In other words, we can say that, a rectangle is a parallelogram with four right angles. A parallelogram can be rectangle only if its angles are right angles.
A parallelogram is a quadrilateral which has two pairs of equal, opposite and parallel sides. A rectangle also has the same properties but the difference is that the angles between the adjacent sides are always right angles i-e. 90°.
But in case of parallelogram, the angles are not necessarily right angles. This clearly shows that every rectangle is a parallelogram. In other words, we can say that, a rectangle is a parallelogram with four right angles. A parallelogram can be rectangle only if its angles are right angles.
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