### Quadrilateral - Wikipedia

basis ofspecific attributes. Use Venn diagrams to classifir quadrilaterals squares. They do not need to have examined the relationships among these figures. Here are examples of some of the different types of quadrilaterals. and some properties are consequences of these definitions (e.g., opposite sides of a 3 Draw Venn diagrams to show the relationships between the following sets (in some. Encyclopedia of Quadri-Figures by Chris Van Tienhoven; Compendium of quadrilaterals and Definition and properties of tetragons from Venn Diagram Quadrilaterals expressed in the form of a Venn diagram.

One, two, three, four. That is a quadrilateral. These are all quadrilaterals. They all have four sides, four vertices, and, clearly, four angles. One angle, two angles, three angles, and four angles.

Actually, let me draw this one a little bit bigger, because it's interesting. So in this one right over here, you have one angle, two angles, three angles, and then you have this really big angle right over there.

If you look at the interior angles of this quadrilateral. Now, quadrilaterals, as you can imagine, can be subdivided into other groups based on the properties of the quadrilaterals.

And the main subdivision of quadrilaterals is between concave and convex quadrilaterals. So you have concave, and you have convex. And the way I remember concave quadrilaterals, or really concave polygons of any number of shapes, is that it looks like something has caved in. So, for example, this is a concave quadrilateral. It looks like this side has been caved in. And one way to define concave quadrilaterals-- so let me draw it a little bit bigger, so this right over here is a concave quadrilateral-- is that it has an interior angle that is larger than degrees.

So for example, this interior angle right over here is larger than degrees.

### Polygons - Quadrilaterals - In Depth

And it's an interesting proof. Maybe I'll do a video. It's actually a pretty simple proof to show that, if you have a concave quadrilateral, if at least one of the interior angles has a measure larger than degrees, that none of the sides can be parallel to each other.

The other type of quadrilateral, you can imagine, is when all of the interior angles are less than degrees. And you might say, wait-- what happens at degrees? Well, if this angle was degrees, then these wouldn't be two different sides, it would just be one side. And that would look like a triangle. But if all of the interior angles are less than degrees, then you're dealing with a convex quadrilateral. So this convex quadrilateral would involve that one and that one over there.

So this right over here is what a convex quadrilateral could look like-- four points, four sides, four angles. Now, within convex quadrilaterals, there are some other interesting categorizations. So now we're just going to focus on convex quadrilaterals, so that's going to be all of this space over here. So one type of convex quadrilateral is a trapezoid. And a trapezoid is a convex quadrilateral, and sometimes the definition here is a little bit-- different people will use different definitions.

So some people will say a trapezoid is a quadrilateral that has exactly two sides that are parallel to each other.

## Intro to quadrilateral

So, for example, they would say that this right over here is a trapezoid, where this side is parallel to that side. Now I said that the definition is a little fuzzy, because some people say you can have exactly one pair of parallel sides, but some people say at least one pair of parallel sides.

So if you use the original definition-- and that's the kind of thing that most people are referring to when they say a trapezoid, exactly one pair of parallel sides-- It might be something like this. But if you use the broader definition of at least one pair of parallel sides, then maybe this could also be considered a trapezoid so you have one pair of parallel sides like that and then you have another pair of parallel sides like that.

So this is a question mark where it comes to a trapezoid. A trapezoid is definitely this thing here, where you have exactly one pair of parallel sides. Depending on people's definition, this may or may not be a trapezoid. If you say it's exactly one pair of parallel sides, this is not a trapezoid, because it has two pairs.

If you say at least one pair of parallel sides, then this is a trapezoid. So I'll put that in a little question mark there. But there is a name for this, regardless of your definition of what a trapezoid is.

If you have a quadrilateral with two pairs of parallel sides, you are then dealing with a parallelogram. So the one thing that you definitely can call this is a parallelogram. And I'll just draw it a little bit bigger.

So it's a quadrilateral, and if I have a quadrilateral, and if I have two pairs of parallel sides. So the opposite sides are parallel. Trapezia UK and trapezoids US include parallelograms. Isosceles trapezium UK or isosceles trapezoid US: Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.

**Grade 5 Math #11.3, Quadrilaterals, Rectangle, Square, Parallelogram, Rhombus, Trapezoid**

Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Parallelograms include rhombi including those rectangles we call squares and rhomboids including those rectangles we call oblongs. In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles. An equivalent condition is that the diagonals perpendicularly bisect each other.

Not all references agree, some define a rhomboid as a parallelogram which is not a rhombus. An equivalent condition is that the diagonals bisect each other and are equal in length.

Rectangles include squares and oblongs. 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.