The diagonals of a rectangle are congruent, and, again, since a rectangle is a parallelogram, the diagonals bisect each other, making each half the same length:Įach diagonal of a rectangle also divides the rectangle into two congruent right triangles: Since the three special quadrilaterals we’re talking about are all parallelograms, they will all have bisecting diagonals. Or we could use tick marks to show that the diagonals have been bisected: We could add some numbers to illustrate this better… In other words, they cut each other in half. Here’s our regular, non-special parallelogram with the diagonals shown:Īs you can see, the diagonals of a parallelogram bisect each other. A diagonal is a line segment connecting opposite vertices, or corners, of a quadrilateral. Okay, now let’s explore the diagonals of these four quadrilaterals. Not every parallelogram is a rectangle and not every rhombus is a square. Every square is also a rectangle and every rectangle is a parallelogram. Every square is a rhombus and every rhombus is a parallelogram. Here, we’ve arranged our quadrilaterals into a sort of “tree”, starting with the square as the trunk. So let’s recap our quadrilaterals before we start exploring their diagonals: It’s another shape we all know well: the square!Īs you can see, the opposite sides are parallel, all the angles are right angles, and all the sides are congruent. Our last special parallelogram is a rectangle and a rhombus at the same time, so it has the right angles of the rectangle and the congruent sides of the rhombus. Note that the tick marks are all the same, which tells us that all the sides are the same length. It has all the properties of the parallelogram but all of the sides of a rhombus are congruent. Properties of a RhombusĪnother special parallelogram is a rhombus. In fact, they are all right angles, which means they measure 90 degrees. What makes a rectangle a special parallelogram is that its interior angles are the same. That means that the opposite sides are both parallel and congruent, just like our first parallelogram. But one thing we don’t usually think about is that rectangles are just a special kind of parallelogram. The opposite sides of a parallelogram, marked by green tick marks, are congruent, which means they have the same measure.Ī rectangle is a shape we all know well since it appears in the real world so often. The blue arrows denote which sides are parallel to each other. Types of Quadrilaterals Properties of a ParallelogramĪ parallelogram is a quadrilateral that has two sets of parallel sides. A polygon is a shape with multiple sides. Let’s get started!Īll of the shapes that we are going to look at today are quadrilaterals, meaning they are all four-sided polygons. Hi, and welcome to this video on diagonals! Today we’re going to explore the diagonals of parallelograms, rectangles, rhombi, and squares, and see how these shapes relate to each other overall.
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