PCs or Result

The rectangle and the parallelogram are both quadrilaterals, which means that they are both polygons with four sides. The question is, do rectangles count as parallelograms? On the other hand, are parallelograms regarded as rectangles? Here is a quick review of the different properties of both parallelograms and rectangles to help you understand them better.

The parallelogram is a quadrilateral that has:

·         Two pairs of parallel sides

·         Two pairs of opposite sides that are coincident

A rectangle is a quadrilateral that has:

·         Four right angles

·         Two different pairs of opposite sides

Rhombuses are quadrilaterals that have:

·         Four sides of equal length

·         Two pairs of equal opposite angles

Properties of a Rectangle vs. a Parallelogram

There are four right angles in a rectangle. These angles are all congruent with one another. In the rectangle, the vertices join the adjacent sides at a 90° angle, indicating that the opposite sides are parallel lines. A rectangle has all of the properties of a parallelogram since it has two series of parallel sides and two sets of opposite sides that are both congruent. For this reason, a rectangle is always a parallelogram.

It is important to note, however, that not all parallelograms are rectangles. An example of a parallelogram that does not have four right angles can be seen below. In the next section, we will discuss these shapes properties.

Properties of a Rectangle vs. a Rhombus

We defined a rhombus above, which is the shape pictured above. In view of the similarity between a rhombus and a rectangle, let’s talk about the similarities between the two shapes.

Besides, a rectangle may not always be a rhombus. There are two sets of congruent sides on a rectangle whereas there are four congruent sides on a rhombus.

Can I ask if rhombuses are always parallelograms? Yes, they are always parallelograms! It is true that the two pairs of opposite angles of a rhombus are always equal, just as the two pairs of opposite angles of a parallelogram are always equal. In other words, a rhombus is just a special case of a parallelogram that happens to also have congruent angles on all four sides.

Is a Rectangle a Parallelogram?

All quadrilaterals have a certain property, whether they are rectangles, parallelograms, or rhombuses.

A parallelogram is a quadrilateral that has:

·         Two pairs of parallel sides

·         Two opposite pairs of sides that are congruent

A rectangle is a quadrilateral that has:

·         Four right angles

·         Two pairs of opposite sides that are congruent

The characteristics of a rhombus are:

·         Four sides of equal length

·         Two pairs of equal opposite angles

In addition to the types of quadrilaterals we have described here, there are many other types of quadrilaterals. As a result, you now know the answer to the question “Is a rectangle a parallelogram?”.” A rectangle is always a parallelogram. It is not necessarily the case that a parallelogram is always a rectangle.

As part of our series on math’s we will focus on answering the question “What is a line of symmetry? And what is its significance and what are its purposes?” as well as giving you all the information you need to help your child understand this small section of the math’s curriculum! Make sure you scroll all the way to the bottom of the blog so that you can find some practice questions for your child to test their skills.

For example, if you cut an apple into two equal halves, then that apple piece is said to be in symmetry with the one next to it. The second example that I would like to give is that if we cut an equilateral triangle into two equal halves, then the two triangles that form after the intersection are right-angled triangles. For line symmetry there are a few more examples, such as square, rectangle, circle, which can also be considered.

Throughout this blog, we will be providing information and resources designed to help parents, teachers, and caregivers to support home learning and find resources to support home learning during the Covid-19 epidemic and beyond.

Introduction of Line of Symmetry

The line of symmetry is an imaginary line that exactly cuts a shape in half.  This means that if you fold the shape along the line, both halves of the shape would match up exactly. In the same way, it would not change the shape if you decided to place a mirror along the line.

There are four lines of symmetry in a square, as shown in the following illustration.

The symmetry of an equilateral triangle consists of three lines.

Symmetry Lines in Different Symmetrical Shapes

We will be teaching your child about the different shapes and their respective lines of symmetry, but for now, let’s look at some of the most common shapes.

Learning About Symmetry in Primary School

A teacher might ask the child to draw lines of symmetry on the following shapes provided to him or her in Year 2 as an introduction to symmetry. The most common way to make it easier for children to be clear is to give them a cutout shape which they can fold in half so that they can see clearly that both sides of the shape are the same:

Children are asked in Year 4 to identify lines of symmetry in two-dimensional shapes that have been presented in different orientations. The students will need to be aware that shapes can have more than one symmetry line. It may be asked of the students to examine these regular shapes and consider how many lines of symmetry they can find in them. In this instance, it is helpful for them to cut out the shapes and fold them in half, then look at how many folds have been made.

You may also ask the students to classify shapes according to various properties, such as line symmetry. It is possible to give the students a collection of shapes and ask them to place them into a Carroll diagram in the following manner:

The children in the fifth grade begin to reflect shapes in a mirror line. It may be necessary for students to complete the shading in a shape after reflecting it in a mirror line, or for them to draw half of a shape after reflecting it with a mirror line. The shape is usually provided on squared paper in order to allow the students to complete the shape accurately.

Reflected shapes in a mirror line

There will also be an exercise where the children will be given a quarter of a shape and will then be asked to reflect it in two mirror lines, such as:

As an alternative, they can be shown a shape with shaded squares reflected from two mirror lines, and asked to complete the shading of the squares.

Piecewise-defined functions are functions defined by multiple sub-functors that each apply to a different interval within the domain, also called piecewise functions, hybrid functions, or definitions by cases. Rather than being a characteristic of the function, a piecewise definition is a way of expressing the function.

There is a different but related notion of a property holding piecewise in a function, which is used when the domain can be divided into intervals on which the property holds. It is important to note that this is not a property of the notion above, but a property of the function itself. We will use the example of a piecewise linear function (which happens to be a continuous function as well).

Defined Piecewise-Graph Functions

There are times when we come across a function that requires more than one formula in order to obtain the desired results. For example, in the toolkit functions, we introduced the absolute value function f(x)=∣x∣. When the domain is made up of all real numbers, and the range includes all values greater than or equal to 0, the absolute value is the magnitude, or modulus, of any real number. The distance on the number line from 0 is the absolute value. It is essential that the output exceed or equal 0 in each of these definitions.

If we enter 0, or a positive number, the output is the same as the input.

• f(x)=x if x≥0

Inputs with negative values result in the opposite output.

• f(x)=−x if x<0

The absolute value function can be thought of as a piecewise function given that it requires two different processes or pieces to function. Essentially, a piecewise function refers to a function that uses more than one formula to define the output over a set of different pieces of the domain.

Continuity And Differentiability of Piecewise Functions

The following conditions must be met for a piecewise function to be continuous on a given interval in its domain:

• Functions of its constituent parts are continuous over the intervals (subdomains);
• At each endpoint of the subdomains within that interval, there is no discontinuity.
• For example, the pictured function is piecewise continuous within each subdomain, but not continuously throughout the entire domain due to the discontinuity at x_o. This position uses the value of the right function piece as indicated by the filled circle.

The following conditions have to be met in addition to those pertaining to continuity for a piecewise function to be differentiable in its domain:

• Each of its constituent functions can be differentiated on the corresponding open intervals,
• there are one-sided derivatives at each interval endpoint,
• The one-sided derivatives of two neighboring subintervals coincide when two subintervals touch.

Specific Types of Mathematical Functions

The same is true for career paths, as there are many different types of functions. A piecewise function is an example of a mathematical function. There are different parts to a piecewise function. The piecewise function has many parts, each of which has a specific job it performs when the conditions are met.

For example:

• f(x) = x – 2, x < 3
• f(x) = (x – 1)2, x ≥ 3

If this function is invoked with a <3 input, it behaves differently from when it is invoked with a ≥ 3. The absolute value function is the most common piecewise function.

Examples of Piecewise Functions

Here are some more examples of piecewise functions that you might find useful. This shows that they do not have to be restricted to only two equations, they can have a lot of parts as well.

For example:

f(x) = 4 – x, x ≤ -4

f(x) = (x + 2)/2, x > -4

Orhow about:

f(x) = -3, x > 1

f(x) = -2x, x = 1

f(x) = x/2, x < 1

And how about this one:

f(x) = -x, x < 0

f(x) = x2, 0 ≤ x < 4

f(x) = x – 5, 4 ≤ x < 6

f(x) = x/2, x ≥ 6

The radius formula can simply be derived by halving the diameter of the circle. If we make a line segment that connects a point on the circumference of a circle to the exact center of the circle, then the line segment that we make is called the radius of the circle. It is the distance between the center of a circle and the circumference of the circle that is called its radius. In all cases, the diameter is twice the radius. This means that the diameter is divided by two in order to obtain the formula.

Intro of Radius

In geometry, a radius is defined as the line segment connecting the center of a circle or sphere with its circumference or boundary. This is generally abbreviated as ‘r’, which is an important part of circles and spheres. Whenever we talk about more than one radius at a time, we use the plural “radii”. In circles or spheres, the diameter is the longest line segment connecting any two points lying on the opposite side of the center, and the radius is half the diameter. This can be expressed as d/2, where d is the diameter of the circle or sphere. The image below shows the relationship between diameter and radius for a circle.

With the given information, let’s learn how to calculate the radius’s length using the formulas.

Formulas for Radius

Radius Formula in terms of diameter, circumference, and area is as follows:

Radius Formulas

Radius in Terms of Diameter   d ⁄ 2

Radius in Terms of Circumference    C ⁄ 2π

Radius in Terms of Area √(A ⁄ π)

Where,

• r is the radius of the circle
• d is the diameter of the circle
• C is the circumference of the circle
• A is the area of the circle

The Radius of a Circle – How to Find

There are three basic formulas for finding a circle’s radius, i.e., when the diameter, area, or circumference are known. Here is the formula for finding the radius of a circle

• If you know the diameter, the formula is Radius = Diameter/2.
• When the circumference of an object is known, the radius can be calculated by using Radius = Circumference/2π.
• For an area of a circle that is known, the radius can be calculated using the formula Radius =⎷(Area of the circle/π).

As an example, if we specify 24 units for the diameter, then the radius will be 24/2 = 12 units. A circle’s radius can be calculated as 44/2π if the circumference of the circle is 44 units. This implies, (44×7)/(2×22) = 7 units. And, if the area of a circle is given as 616 square units, then the radius is ⎷(616×7)/22 = ⎷28×7 = ⎷196 = 14 units.

Radius of a Sphere

An object that is 3D solid is a sphere. It is the segment from any point on the boundary of the sphere to its center. It is a determining factor when drawing a sphere, since its size is determined by its radius. A sphere can have an infinite number of radii and they will all have the same length, just as circles do. We need to know the radius of a sphere in order to calculate its volume and surface area. Our formulas for volume and surface area make it easy to calculate the radius of the sphere.

Radius of the sphere from volume = 3⎷(3V)/4π units, where V represents the volume and the value of π is approximately 3.14.

Radius of a sphere in surface area units = ⎷(A/4π) units, where A represents the surface area.

Use our free online sphere radius calculator to calculate the radius given a volume, surface area, or diameter of a sphere.