Rectangles, Rhombuses, and Squares | Wyzant Resources
In this lesson we are going to deal with definition of parallelogram, rectangles, square, rhombus and trapezoid. Further we are going to understand how to. Copy of SIMILARITIES AND DIFFERENCES OF SQUARE,RHOMBUS AND RECTANGLE. A Rhombus is a quadrilateral; A Square is also a quadrilateral. Opposite sides of Hence you can observe the similarities between Rhombus and Square.
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.
Rhombus vs Square - Difference
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. 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.
Difference between a Rhombus and a Square
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.
- Difference Between Square & Rhombus
- Quadrilaterals Properties | Parallelograms, Trapezium, Rhombus
- Difference Between Square and Rhombus
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: Let's examine the information we have been given from the exercise, in order to deduce more information from it.
We know that EKIN is a parallelogram, and that?
Since EKIN is a parallelogram, we know that its opposite sides are parallel. Therefore, segments EK and IN are parallel. Next, we can use the Alternate Interior Angles Theorem to claim that? Recall, that the alternate interior angles are congruent if and only if a transversal intersects a pair of parallel lines. By transitivity, we can say that?
Let's look at our chain of congruences to be assured that the previous statements are true. The diagonal splits our parallelogram into two triangles. In fact, because two angles of each triangle are congruent, we can say that? INK are isosceles triangles. The converse of the Isosceles Triangle Theorem states that the sides opposite of congruent angles of isosceles triangles are congruent, so we know that segment EK is congruent to segment EN, and that segments IK and IN are congruent.
By transitivity, we know that EN? Let's look at our new illustration. To distinguish a rectangle from square following property should be kept in mind: Only opposite sides of a rectangle are equal unlike square which has all sides equal. To distinguish a rectangle from rhombus following property should be kept in mind: Each angle of rectangle is 90 degrees unlike rhombus where angles are not equal to 90 degrees.
Rhombus If all sides of parallelogram are equal but angles are not equal to 90 degrees, then this parallelogram is called a rhombus. Rhombus and square have all sides equal, to distinguish a rhombus from square following property should be kept in Each angle of square has to be 90 degrees unlike rhombus. Each angle of rectangle has to be 90 degrees unlike rhombus. Unlike rhombus only opposite sides of rectangle are equal. A square is a parallelogram with right angles and equal sides. A square is a particular case of a rectangle and a rhombus simultaneously.
So, it shows both the properties of rhombus and rectangle simultaneously. Square can be differentiated from a rectangle and rhombus due to following properties.