Question

Question #7ede7

Answer 1

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.

Answer 2

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).

1. Unlike a parallelogram, Rhombus has opposite sides not only parallel and equal, but also all the four sides are equal.

2. Unlike a parallelogram, diagonals not only bisect each other, but also intersect at right angles in a rhombus.

3. 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.

4. Like rectangle which is a specific case of a parallelogram with vertices being right angles, square is a specific case of a rhombus.

5. In effect, rectangles and squares are special forms of cyclic quadrilaterals where as parallelograms and rhombuses are not cyclic quadrilaterals

6. 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