# Trapezoid and rhombus relationship help

### Quadrilaterals Properties | Parallelograms, Trapezium, Rhombus | MBA Crystal Ball A rectangle has two pairs of opposite sides parallel, and four right angles. We can use a Venn diagram to help us group the types of quadrilaterals. A Venn diagram uses overlapping circles to show relationships between groups of objects. Rhombus: A quadrilateral with four congruent sides; a rhombus is both a kite and a Rectangle: A quadrilateral with four right angles; a rectangle is a type of. In this tutorial on basic geometry concepts, we cover the types and properties of quadrilaterals: Parallelogram, rectangle, square, rhombus.

## Difference Between Rhombus and Parallelogram

An equivalent condition is that opposite sides are parallel a square is a parallelogramthat the diagonals perpendicularly bisect each other, and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle four equal sides and four equal angles. This implies that one diagonal divides the kite into congruent trianglesand so the angles between the two pairs of equal sides are equal in measure.

It also implies that the diagonals are perpendicular. A convex quadrilateral is tangential if and only if opposite sides have equal sums. It is a type of cyclic quadrilateral. A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. A dart or arrowhead is a concave quadrilateral with bilateral symmetry like a kite, but one interior angle is reflex. So it's a parallelogram, which tells me that opposite sides are parallel.

And then if we know that all four angles are 90 degrees. And we've proven in previous videos how to figure out the sum of the interior angles of any polygon. And using that same method you could say that the sum of the interior angles of any quadrilateral is actually degrees. And you see that in this special case as well. But maybe we'll prove it in a separate video. But this right over here we would call a rectangle.

Parallelogram-- opposite sides parallel and we have four right angles. Now, if we have a parallelogram where we don't necessarily have four right angles, but where we do have the length of the sides being equal, then we're dealing with a rhombus. So let me draw it like that. So it's a parallelogram. This is a parallelogram, so that side is parallel to that side, this side is parallel to that side.

And we also know that all four sides have equal length. So this side's length is equal to that side's length, which is equal to that side's length, which is equal to that side's length.

### Difference Between Rhombus and Parallelogram (With Comparison Chart) - Key Differences

Then we are dealing with a rhombus. So one way to view it-- all rhombi are parallelograms. All rectangles are parallelograms. All parallelograms you cannot assume to be rectangles. All parallelograms you cannot assume to be rhombi. Now, something can be both a rectangle and a rhombus. So let's say that this is the universe of rectangles. So the universe of rectangles-- I'll draw a little bit of a Venn diagram here-- is that set of shapes and the universe of rhombi is this set of shapes right over here.

So what would it look like? Well, you would have four right angles and they would all have the same length. So it would look like this.

Properties of a rhombus, rectangle, and a square

So it'd definitely be a parallelogram. Four right angles and all the sides would have the same length. And this is probably the first of the shapes that you learned, or one of the first shapes.

This is clearly a square. So all squares could also be considered a rhombus, and they could also be considered a rectangle, and they could also be considered a parallelogram.

But clearly, not all rectangles are squares, and not all rhombi are squares. Opposite sides have equal length. Diagonals The diagonals bisect each other at right angles forming scalene triangle. The diagonals bisect each other forming two congruent triangle.

It is flat shaped and has four sides; wherein the facing sides are parallel to one another see figure given below. The opposite angles of a rhombus are equal i. Its diagonals meet each other at 90 degrees right angletherefore, perpendicular to each other and forms two equilateral triangles. Its adjacent sides are supplementary, which means that the sum of their measure is equal to degrees. It is also known as an equilateral parallelogram.