All Equal To

The Mathematical Symbol "All Equal To (≌)"

Understanding the ≌ Symbol in Mathematics

The mathematical symbol ≌ represents the concept of "All Equal To" or "isomorphically equivalent to". This symbol often appears in the realm of geometry and algebra to depict situations where two entities share an identical structure or form. Below, we will discuss two primary uses of this symbol, offering two examples for each.

1. Geometry

In the context of geometry, ≌ is used to signify that two figures are congruent, meaning they have the same size and shape.

• Example 1: If triangle ABC is congruent to triangle DEF, we write it as triangle ABC ≌ triangle DEF.
• Example 2: Two circles with the same radius are congruent. If circle O with radius 5 units is congruent to circle P with radius 5 units, it can be written as circle O ≌ circle P.

2. Algebra and Advanced Mathematics

In algebraic contexts and some other advanced areas of mathematics, the symbol may represent isomorphic structures, indicating that two algebraic structures are essentially the same.

• Example 1: In group theory, if two groups, G and H, are isomorphic, it means they have the same structure. We express this as \( G ≌ H \).
• Example 2: If two rings, R and S, share the same algebraic structure, then R ≌ S.

In summary, the ≌ symbol's meaning is rooted in the context it's used. Whether it's to convey congruence in geometric figures or isomorphic equivalence in algebraic structures, understanding the situation is key to deciphering its intended use.

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Codes for the ≌ Symbol

The Symbol	≌	copy
Alt Code	Alt 8780	copy
HTML Code	≌	copy
HTML Entity	≌	copy
CSS Code	\224C	copy
Hex Code	≌	copy
Unicode	U+224C	copy

How To Insert the ≌ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ≌ symbol is to copy and paste it into your document. (Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or �.)

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8780. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML Text	Output
<b>My symbol: &#8780;</b>	My symbol: ≌

(Method 4) Use the HTML Entity Code (for webpages).

HTML Text	Output
<b>My symbol: &bcong;</b>	My symbol: ≌

(Method 5) Use the CSS Code (for webpages).

CSS and HTML Text	Output
<style> span:after { content: "\224C";} </style> <span>My symbol:</span>	My symbol: ≌

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML Text	Output
<b>My symbol: &#x224C;</b>	My symbol: ≌

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x224C to place the ≌ symbol on your canvas. For example:

JavaScript Text
const x = "0x"+"E9" ctx.fillText(String.fromCodePoint(x), 5, 5);
Output
≌

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ≌ is U+224C. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:

Type	Output
224C [Hold down Alt] [Press x]	≌ (The 224C turns into ≌. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u224C. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u224C" document.write("My symbol: " + str)	My symbol: ≌