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How A Theorem, A Lemma, A Corollary are different from each other?

In mathematics, some great mathematicians have given names to mathematical equations which have exactly four labels if the equations are to be true. Now, you all must be confused about what context am I talking about? We all have heard these terms once in our life ‘Theorem’, ‘Lemma’, and ‘Corollary’ while studying math, and if an equation of mathematics is true then it is labeled with these three terms.

And, also you must have used these terms while solving an equation if it has been proven then we needed to write these terms. So, now what exactly this means is a major question here. As most of us don’t know the meaning of these terms.

If explained thoroughly then more or less these three terms have the almost same meaning. In the sense, that if the equations are true including some axioms. But still, mathematicians have used different names for different equations as these terms have some narrow differences.

Here we are explaining some terms which will help you understand the difference between theorem, lemma, corollary.


connected by the (=) equal symbol an equation is a mathematical statement that includes two arithmetical expressions. This describes that the two expressions on both sides are equal to each other.


axioms are statements or propositions based on assumptions that are believed to be true without any proof. Considered to be the basic building blocks through which the theorems have been proved. For instance, a perfect example for Axiom can be 2+2 = 4 now this doesn’t need any more proof, but it is self-evidence.

Difference between Theorem, Lemma, and Corollary

Now let’s see the difference between all these three terms in a very easy way so that all of you can understand easily.


A theorem is the most common term which we must have used in studying mathematics. Stating a theorem is a geometrical or mathematical calculation that is proven to be correct which includes some mathematical statements which are proven true.

If we compare lemma and corollary with a theorem it is considered to be the most important and which has primary proofs. However, a lot of mathematicians have said that if we differentiate between theorem and lemma then it would go very subjective. e-Day : Fun Mathematical Days you Need to Know About

A perfect example for a theorem is ‘nevertheless how many times you try to divide an angle on the straight line, the segments of the angle will always add up to 180 degrees.’


It is said that a corollary is much easier to understand than to understand a theorem and a lemma. The corollary is considered to be direct proof that relies highly on a particular theorem. For example, we usually say that this corollary is of Theorem A. in some of the cases corollaries are a reverse proof of the theorem. Seventeen Facts about 17

For instance, if it is stated in a theorem that two opposite angles which are between two parallel lines and are intersected by other lines turn out to be true always. The corollary in this would be that these lines are always going to be parallel if the angles which are opposite if created by the intersection of a third line are going to be equal.


Lemma as I mentioned above is a bit more tricky to understand than corollary. Lemma is known as a mathematical statement that is proven to be true with the use of some axioms and it also helps in proving other theorems correct.

Now, you must be confused as theorems and lemma are almost the same. But still, the single difference between a theorem and a lemma is that it can be subjective for some of you. But it is that theorems are given higher priority than lemma. And that’s why we said that it’s a subjective point and it may differ from individual to individual but through an example, we can try to clear the point. Cool Fact about Eighteen

For example, if an angle is inscribed on the circumference of a circle then it’ll always be half of the angle created at the center of a circle. This statement has a lot of importance so this is a theorem and can be used for proving the other theorems.

However, this theorem’s lemma would go like if a diameter is formed from the central angle, then the angle which is inscribed at the circumference of the circle would always be a right angle. Did you know about Interesting Facts of the Number 20?


So, these were all the differences between a theorem, a lemma, and a corollary. These three terms might not have much difference but it is very important to even understand the minor difference. Interesting Mathematical story : Can you tell me the 100 word without A B, C, and D

This was all for this article. We hope that this information was helpful for you all. If you have any related queries drop them in the comments. Thank you!

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