Question #7ede7
2 Answers
Yes
Explanation:
A rhombus has all its sides equal.
A parallelogram has both pairs of opposite sides parallel.
Having equal sides ensures that a rhombus will have parallel opposite sides. This makes it a parallelogram.
If we cut a rhombus by its diagonal, we will have a 2 equivalent isosceles triangles. From the properties of triangles, we can conclude that the opposite angles of a rhombus are always equal.
If opposite angles of a quadrilateral are equal, it would follow that the opposite sides will be parallel. This makes a rhombus a parallelogram.
Differences are listed in the explanation.
Rhombus - special parallelogram - opposite sides parallel & all four sides equal.
Rectangle -specific case of parallelogram and
Square - specific case of a rhombus.
Explanation:
Rhombus like a parallelogram is a quadrilateral (a four sided figure).
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Unlike a parallelogram, Rhombus has opposite sides not only parallel and equal, but also all the four sides are equal.
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Unlike a parallelogram, diagonals not only bisect each other, but also intersect at right angles in a rhombus.
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Like a parallelogram, area is given by the formula b * h, where b is the side and h is the height; in addition, area of a rhombus can be calculated using the diagonals and the formula is ((1/2) * d1 * d2) where d1 & d2 are the diagonals.
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Like rectangle which is a specific case of a parallelogram with vertices being right angles, square is a specific case of a rhombus.
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In effect, rectangles and squares are special forms of cyclic quadrilaterals where as parallelograms and rhombuses are not cyclic quadrilaterals
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Kites have diagonals intersecting at right angles similar to rhombuses, but the diagonals are not bisecting each other, so also opposite sides are not para and equal; rather, adjacent sides are equal.
Rhombus
Square
Kite
Parallelogram
Rectangle