Watch this video lesson to learn why rhombuses are a special type of quadrilateral. Also, learn why a rhombus is also a parallelogram. Watch as we explore the sides and angles of a rhombus.
What is a Rhombus?
What is a rhombus? It is simply a four-sided flat shape whose sides are all the same length and whose opposite sides are parallel. Try to picture this in your head or, better yet, go get four toothpicks. Pause the video if you need some time to get the toothpicks. Place the four toothpicks on a flat surface. Start by moving two toothpicks so that they are parallel to each other. Then, connect the other two toothpicks so that it closes your shape. You may have to move the first toothpick you placed to allow room for the side toothpicks to fit. Just keep in mind that you want to keep your sides parallel to each other.
Congratulations! You have just created a rhombus! Do you see how all the sides are the same length? Also, do you see how the opposite sides of the rhombus are parallel to each other? Try moving the toothpicks around but keeping the sides parallel to each other and all the ends touching each other. All these other shapes that you come up with are still rhombuses.
All rhombuses fall under the category of quadrilaterals, a flat shape with four sides. What makes rhombuses special is that all four of the sides are all the same length. If you are given the length of just one side of a rhombus, then you also know the measurement of all the other sides because of this property. This is the identifying property of a rhombus.
Another identifying property of a rhombus is that the opposite sides are parallel to each other. Because of these two identifying properties, a rhombus also falls under the category of a parallelogram, a four-sided flat shape whose opposite sides are parallel and of equal length. Yes, all rhombuses are parallelograms, but not all parallelograms are rhombuses. This is because the definition of a parallelogram is more lenient than that of a rhombus, so you can have parallelograms where not all four sides are equal in length to each other.
Now let's look at the angles of a rhombus. Just like all four-sided shapes, our rhombus has four angles. Do you see anything unique about the angles as you move your toothpicks into various other rhombus shapes? You might have noticed that you always have two pairs of opposite angles that are equal to each other. If you were standing with your back against one angle and facing towards the middle of the shape, the opposite angle is the angle directly in front of you and the one that you would be staring at directly. Looking at various rhombus shapes below, can you spot these opposite pairs of equal angles? All rhombuses have the property that the opposite angles are equal to each other.
In all rhombuses, opposite angles are equal.
Another property that all rhombuses have is that if you draw your diagonals, the lines connecting your opposite angles with each other, then the point where the diagonals intersect produces right angles. Also, the point of intersection is the bisection of the diagonals, meaning that the intersection point happens to be the midpoint of each diagonal.
What have we learned? We've learned that rhombuses are four-sided shapes whose sides are all equal to each other and whose opposite sides are parallel. We've learned that these shapes also fall under the categories of quadrilaterals, four-sided flat shapes, and parallelograms, four-sided flat shapes whose opposite sides are parallel and of equal length. Just because a rhombus is a quadrilateral and a parallelogram, it does not mean that a quadrilateral or parallelogram is a rhombus.
The properties of rhombuses are that they have four equal sides with two pairs of opposite sides that are parallel to each other. There are also two pairs of opposite angles that are equal to each other. When you draw the two diagonals of a rhombus, these two diagonals bisect each other and will form right angles at their point of intersection.
After this lesson, you should be able to:
- Define rhombus
- Describe the properties of a rhombus
- Indicate which property is the identifying property