In childhood, you learn a lot of things in the classroom, and there’re many you’ve wondered, “Is this relevant?”, “ What are the uses of these mathematical concepts?”, “Will it help me in real life?” and many more. One way or another, you’re not wrong for asking that question. We all have been there at some point in our life.
Now let’s talk about class 10. Class 10 is one of the most crucial phases in a student’s life. Students will have to select their specialization as their future, so it is essential to resolve all the queries before moving on to the next grade. Maths Formulas are very necessary for grade 10 students.
Today we’ll ponder a piece of information with you guys that will clear your doubt. In this article,
All the Mathematical Theorems of Class 10 and Their Real-life Applications.
1. Pythagoras Theorem
The theorem states, “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the square of the base side and the square of the perpendicular of the triangle.”
Formula- Hypotenuse2 = Base2 + Perpendicular2
H2 = B2 + P2
Real-Life Application- It helps you to calculate the diagonal’s length connecting them.
- This application is used in architecture or construction work.
- It is also used in navigation to find out the shortest distance between the initial point and the final destination.
- Pythagoras is also helpful in surveying while creating a map.
Note: You can use Maths Symbols to understand the mathematical concepts.
2. Midpoint Theorem
The theorem states, “The line segment in a triangle joining the midpoint of the two sides of a triangle is said to parallel to its third side and also is half of the length of the third side.”
Formula- Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Real-Life Application- It helps to find out a midpoint of any particular area
- A real-life example of a midpoint is the equator.
- You can also mark a specific meeting point with the help of a midpoint.
- It is also used in the measurement process of anything.
3. Bayes Theorem
The theorem states, “ The conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.”
Formula- P(A|B) = P(B|A) P(A) / P(B)
Real-Life Application- There’re certain situations where you can use Bayes Theorem.
- It is used for the testing of the rare medical diseases
- With the help of the Bayes Theorem, you can also find information regarding any topic.
- You can also find out your progress report through probability with the help of the theorem.
4. Remainder Theorem
The theorem states, “ When a polynomial p(x) ( who is greater than or equal to 1) is divided by another polynomial q(x) whose zero equals to x = a and the remainder is given by r = p(a)
Formula- p(x)/ x-a = q(x) + r(x)
Real-Life Application- The remainder theorem is helpful in academic life as well.
- It is more efficient than other polynomial theorems.
- The results are accurate with the remainder theorem.
- It is also helpful in mathematical chapters like trigonometry and calculus, which is also helpful in the real world.
5. Angle bisector Theorem
The theorem states, “ An angle bisector of an angle of a triangle divides the opposite sides into two parts that are proportional to the other two sides of the triangle.”
Formula- BD/DC = AB/AC
Real-Life Application- In many places, you can use the Angle bisector theorem
- Architects use the angle bisector theorem while drafting a design.
- While sewing as well, you need the angle bisector theorem to do so.
- One more example of the angle bisector theorem can be quilting, and you can easily do the quilting by using the theorem.
6. Fundamental Theorem of Arithmetic
The theorem states, “Every integer greater than 1 is either a prime number or can be expressed as a prime.”
In other words, all the natural numbers can be expressed in the form of the product of its prime factor.
Real-Life Application- You can use the fundamental theorem of arithmetic in:
- It simplifies the calculations for the students and the people.
- It tells the common grounds for the results.
7. Inscribed Angle Theorem
The theorem states, “ An angle 𝜽 inscribed in a circle is half of the central angle 2𝜽 that subtends the same arc on the circle.”
Real-Life Application- For the Inscribed Angle Theorem, there’re specific examples.
- The inscribed angle theorem can be used in the sniper target grid
- You can also use it to divide a circular figure as well.
Conclusion
These were some real-life uses of the class 10 theorems. We understand that sometimes it might be challenging to understand these theorems, and it seems useless as you’ll not find these theorems in your grades 11 and 12 but everything matters.
You need to understand the concepts clearly to use them in the real world, and for that, you can refer to NCERT Solutions for Class 10 Maths for your reference.
Mathematics is not the most accessible subject but the most scored subject. You need to focus on it and clear your basics to formulate it in your life and career. Try to solve as many problems as you can.
FAQ
Q1. What is a real-life example of a theorem?
Ans. It shows how a mathematical theorem is used in the real world and the meaning of understanding a concept.
Q2. What is the most famous theorem of mathematics?
Ans. The most famous mathematical theorem in the article is the Pythagoras Theorem mentioned above.
Q3. List all the theorems of Class 10.
Ans. There’re seven mathematical theorems are there in class 10:
- Pythagoras Theorem
- Midpoint Theorem
- Fundamental Theorem of Arithmetic
- Bayes Theorem
- Inscribed Angle Theorem
- Angle bisector Theorem
- Remainder Theorem
Q4. What are theorems in mathematics used for?
Ans. A statement that can be demonstrated to be proved as a true statement by various mathematical operations.
Q5. What are the most essential theorems in class 10?
Ans. All the theorems are necessary, but if we compare them and look at the weightage, then Pythagoras Theorem, Midpoint theorem, and the Remainder Theorem can be the most important theorems of Class 10.
