Learn about Relationships between Quadrilaterals In this lesson let’s learn about relationships between quadrilaterals. As we know quadrilateral has four sides. It’s an enclosed figure. A regular quadrilateral has all four sides equal. So first, all quadrilaterals are parallelograms, is that true or false? Well, this is a quadrilateral. A parallelogram means both sets of sides are parallel. This side is parallel to that side, this is parallel to this side. It’s not necessary that a quadrilateral necessarily have both sides parallel. You could have a quadrilateral that looks like this where it’s at four sides but they’re not parallel to each other. So, all quadrilaterals are parallelogram is actually a false statement. All parallelograms have to be quadrilaterals because they’ve got four sides. So, quadrilaterals can either be parallelograms or not parallelograms. If they are parallelograms, if they have both sides that are parallel to each other and also at right angles from each other then they are called rectangles. If all four sides are parallel or perpendicular to each other but also of the same length than their rhombuses, if it’s a rectangle and a rhombus which means it’s right angle, not a right angle all four sides equal, side not equal. If they’re both then it’s a square. Not parallelograms, trapezoids, kites and others will come at this in two second. So first one, all quadrilaterals are parallelograms. Well that’s absolutely false. Let’s look at the second one. All parallelograms are rhombuses. Well, parallelograms maybe rhombuses may not be rhombuses. So a parallelogram, all we know about it is two sides are both the opposite sides are parallel to each other. That’s a parallelogram. It becomes a rhombus if all sides are equal in length. So, as you can see all of these are equal in lengt6h and parallel to each other. This is a rhombus. This is a parallelogram. So all parallelograms are not rhombuses. This also is false. The reason it’s false is because rhombuses are parallelograms but parallelograms are not necessarily rhombuses. All squares are rectangles so let’s look at a square. A square is a rectangle that has equal sides. These are all equal sides. That’s a square. I could also have a rectangle that looks like this. This and this sides are equal. This two sides are equal so all squares are rectangles actually that’s true because a square is also a rectangle. In order for something to be a rectangle, all four sides have to be parallel to the opposite sides and intercept or meet at 90 degree angles. At rectangle, that’s what happens. A square is a rectangle with equal sides. So, this is indeed true. All squares are rectangles. Now, the fourth one, all trapezoids are parallelograms. Well, let’s draw them. Again, what’s a parallelogram? Parallelogram means, I’ve got two sides that are the corresponding sides are parallel to each other and of the same size. So, that’s a parallelogram. This is one angle, this is the other angle. These two sides are parallel, these two sides are parallel. When I look at the trapezoid, a trapezoid has only one set of sides parallel to each other. This A and B are parallel to each other. They’re not of the same length so trapezoids are not parallelograms because both sides of trapezoids are not parallel to each other only one side is. So, this is actually false. Again, let’s go back to the key thing we need to remember. Trapezoids are not parallelograms neither are kites and there are a few others. Quadrilaterals are in the parallelograms or not a parallelogram. This is defined by other sides parallel to each other and is the opposite sides parallel to each other. Both of them have to be parallel. If they are indeed parallel and they intercept at 90 degrees then they’re rectangles. If they intersect not 90 degrees, they’re rhombuses and if a figure is both a rectangle and a rhombus which means it intersects at 90 degrees but all four sides are equal in length, then it’s a square.