True or False: If it is a rhombus, then it is a parallelogram. Could someone explain to me the differences and similarities. I don't get it.
2007-07-25 11:42:21 · 8 answers · asked by Mc K 2 in Science & Mathematics ➔ Mathematics
A rhombus is defined to be:
a quadrilateral with equal length sides.
A parallelogram is defined to be:
a quadrilateral with pairs of parallel sides.
See:
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI35.html
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/defI22.html
Now, they don't seem to have any relationship. What you can figure out though is the following:
In a parallelogram, each pair of parallel sides is the same length.
A parallelogram with equal length sides is a rhombus, automatically. Since there are two pairs of equal length sides, we need only require that the two different lengths become the same.
Any rhombus is a parallelogram.
Therefore, if it is a rhombus, it is a parallelogram (True).
Not all parallelograms are rhombuses. Only parallelograms with equal-sides are rhombuses. The relationship between parallelograms and rhombuses is equivalent (in some sense) to that between rectangles and squares. A rectangle is a rectified (right-angle containing) parallelogram. A square is a rectified rhombus.
2007-07-25 11:58:46 · answer #1 · answered by сhееsеr1 7 · 0⤊ 2⤋
A rhombus is a parallelogram - it is a special type of parallelogram, in the same way that a square is a special type of rectangle. A parallelogram MAY have 4 congruent sides... in which case it's a rhombus ! :-) Think about it... a square is so special, that it's a rectangle AND a parallelogram AND a rhombus!
2016-04-01 02:25:15 · answer #2 · answered by Anonymous · 0⤊ 0⤋
The properties of a parallelogram...
Quadrilateral
Opposite sides congruent
Opposite sides parallel (two pairs of parallel sides)
Opposite angles congruent
Adjacent angles supplementary
Properties of a rhombus...
All properties of the parallelogram (which makes it a parallelogram, also)
Plus...
Adjacent sides congruent (making all sides congruent)
Diagonals bisect each other at right angles
Properties of a rectangle...
All properties of a parallelogram (which makes it a parallelogram)
Plus...
Adjacent angles congruent (making each angle a right angle)
Diagonals are congruent and bisect each other
Properties of a square...
All properties of a Rhombus AND all properties of a rectangle (making a square both a rectangle and a rhombus)
Think of a parallelogram as a rectangle at a tilt... and a rhombus is a square at a tilt. A lot of the more subtle properties dont hold... but a generalized visualization of the sides can be thought of in this way.
2007-07-25 12:04:06 · answer #3 · answered by Anonymous · 0⤊ 1⤋
A parallelogram has OPPOSITE sides equal and parallel.
A rhombus is a special kind of parallelogram in that opposite sides are parallel and ALL sides are equal.
A rhombus is a parallelogram but a parallelogram is not a rhombus.
2007-07-28 06:27:27 · answer #4 · answered by Como 7 · 0⤊ 1⤋
A parallelogram is a quadrilateral which has its opposite sides parallel to each other.
A Rhombus is a quadrilateral that has its opposite sides parallel to each other AND has all of it sides equal. A Rhombus is like a square except it has no right angles.
So it is true that if it's a rhombus it's also a parallelogram ( a special parallelogram that has its four sides equal).
2007-07-25 12:05:36 · answer #5 · answered by ironduke8159 7 · 1⤊ 2⤋
A parallelogram merely is a quadrilateral with opposite sides parallel. A rhombus is a parallelogram with all sides equal. A square is a rhombus with right angles. Like subsets.
2007-07-25 12:04:06 · answer #6 · answered by gugliamo00 7 · 0⤊ 2⤋
A rhombus is a parallelogram with two adjacent sides equal.
2007-07-25 11:45:39 · answer #7 · answered by Anonymous · 3⤊ 1⤋
Well, actually, a rhombus is a parallellogram where *all* of the sides are of equal length.
.
2007-07-25 11:55:09 · answer #8 · answered by tsr21 6 · 0⤊ 1⤋