square is also a parallelogram
give reason
Answers
Answer:
as you know parallelogram has 4and more side.
A parallelogram is a quadrilateral with two pairs of opposite sides.
A square is a quadrilateral whose sides have equal length and whose interior angles measure
90 degree .
From the definition, it follows that a square is a rectangle. In fact, a rectangle is a quadrilateral whose interior angles measure
90 degree .
This is one of the two conditions expressed above for a quadrilateral to be a square, so a square is also a rectangle.
Let's show (the more general fact) that rectangles are parallelograms.
Consider a rectangle
A
B
C
D
. The sides
A
B
and
C
D
are opposite and lie on two parallel lines. In fact, if we consider the line on which
A
D
lies, this is a transverse of the pair of lines. The internal angles in
A
and in
D
are alternate interior angles, and the sum of their measures is
90 degree
+
90 degree
=
180 degree .
This means that the lines through
A
B
and
C
D
have to be parallel.
With the same argument one proves that
B
C
and
A
D
lie on parallel lines, and this proves that every rectangle is a parallelogram.
Another (maybe longer) way of proving this fact is to use the condition on the sides of a square (i.e. that all the sides have equal length) and observe that a square is also a rhombus. Then, by showing that every rhombus is a parallelogram, you found another way of proving that every square is a parallelogram.
Answer:
A square has all the properties of a parallelogram and can therefore be considered to be a parallelogram
Explanation:
The properties of a parallelogram can be stated according to:
the sides
the angles
the diagonals
the symmetry
A parallelogram has:
2 pairs of opposite sides parallel
2 pairs of opposite sides equal
The sum of the angles is
360 degree.
2 pairs of opposite angles are equal
The diagonals bisect each other
It has rotational symmetry of order
2
All of these properties apply to square, so it can be considered to be a parallelogram.
However a square has additional properties as well, so it can be regarded as a special type of parallelogram.
A square has:
2 pairs of opposite sides parallel
All its sides equal
The sum of the angles is
360 degree.
All its angles are equal (to
90 degree )
The diagonals bisect each other at
90 degree .
The diagonals are equal.
The diagonals bisect the angles at the vertices to give
45 degree angles .
4 lines of symmetry
It has rotational symmetry of order
4