# Trapezoid and rhombus relationship

### The Relationships between Quadrilaterals by Bhaavi Patel on Prezi

In this tutorial on basic geometry concepts, we cover the types and properties of quadrilaterals: Parallelogram, rectangle, square, rhombus. An equiangular quadrilateral, i.e. the one with all angles equal is a rectangle. of one from avesisland.info) summarize the relationship between various kinds of. 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.

A quadrilateral may be convex or concave see the diagram below. A quadrilateral that is concave has an angle exceeding o. In either case, the quadrilateral is simple, which means that the four sides of the quadrilateral only meet at the vertices, two at a time. So that two non-adjacent sides do not cross.

A quadrilateral that is not simple is also known as self-intersecting to indicate that a pair of his non-adjacent sides intersect.

The point of intersection of the sides is not considered a vertex of the quadrilateral. The shapes of elementary geometry are invariably convex. Starting with the most regular quadrilateral, namely, the square, we shall define other shapes by relaxing its properties. A square is a quadrilateral with all sides equal and all angles also equal. An equiangular quadrilateral, i. An equilateral quadrilateral, i. In a square, rectangle, or rhombus, the opposite side lines are parallel.

## Quadrilaterals Properties | Parallelograms, Trapezium, Rhombus

A quadrilateral with the opposite side lines parallel is known as a parallelogram. If only one pair of opposite sides is required to be parallel, the shape is a trapezoid. A trapezoid, in which the non-parallel sides are equal in length, is called isosceles. A quadrilateral with two separate pairs of equal adjacent sides is commonly called a kite.

However, if the kite is concave, a dart is a more appropriate term. Kite and dart are examples of orthodiagonal quadrilaterals, i.

A square and a rhombus are also particular cases of this class. The four vertices of a quadrilateral may be concyclic, i. In this case, the quadrilateral is known as circumscritptible or, simpler, cyclic.

If a quadrilateral admits an incircle that touches all four of its sides or more generally, side linesit is known as inscriptible. Rectangles have a couple of properties that help distinguish them from other parallelograms. By studying these properties, we will be able to differentiate between various types of parallelograms and classify them more specifically.

Keep in mind that all of the figures in this section share properties of parallelograms.

### Classification of Quadrilaterals

That is, they all have 1 opposite sides that are parallel, 2 opposite angles that are congruent, 3 opposite sides that are congruent, 4 consecutive angles that are supplementary, and 5 diagonals that bisect each other. Now, let's look at the properties that make rectangles a special type of parallelogram. A rhombus is a quadrilateral with four congruent sides.

Similar to the definition of a rectangle, we could have used the word "parallelogram" instead of "quadrilateral" in our definition of rhombus. Thus, rhombuses have all of the properties of parallelograms stated abovealong with a few others. Let's look at these properties. A square is a parallelogram with four congruent sides and four congruent angles.

Notice that the definition of a square is a combination of the definitions of a rectangle and a rhombus. Therefore, a square is both a rectangle and a rhombus, which means that the properties of parallelograms, rectangles, and rhombuses all apply to squares. Because squares have a combination of all of these different properties, it is a very specific type of quadrilateral.

Look at the hierarchy of quadrilaterals below. This figure shows the progression of our knowledge of polygons, beginning with quadrilaterals, and ending with squares. Notice that there are two arrows pointing to the square. That is because a square has all the properties of a rectangle and rhombus.

Now that we are aware of the properties of rectangles, rhombuses, and squares, let's work on a few exercises that will gauge our understanding of this material. Exercise 1 Identify each parallelogram as a rectangle, rhombus, or a square. First, let's take a look at Parallelogram A.

### Rectangles, Rhombuses, and Squares | Wyzant Resources

The figure shows that it has four congruent sides and that its diagonals intersect perpendicularly. Because its sides are congruent, we know that the parallelogram is not a rectangle. The fact that Parallelogram A's diagonals intersect perpendicularly does not help us because both rhombuses and squares share this characteristic.

The angle at the top of Parallelogram A is not a right angle, however. Therefore, we know that it is not a square. Parallelogram A is a rhombus. In Parallelogram B, we see that there are four right angles and that the pairs of opposite sides are congruent. However, consecutive sides are not congruent, so we can eliminate rhombuses and squares from our options. Thus, Parallelogram B is a rectangle. Let's take a look at Parallelogram C now.

We note that it has a pair of right angles and four congruent sides. Our inclination leads us to think that this parallelogram is a square, but let's make sure just in case.

This tells us that there are actually four right angles in Parallelogram C, so we know that it is a square and a rhombus. We know that ABCD is a rectangle, so let's use some rectangle properties to help us figure out what x is. It appears as though the focus of this exercise is on the diagonals of the figure.

From above, we know that the diagonals of a rectangle are congruent, so let's set segments AC and BD equal to each other: