Everything You Need To Know About Pythagoras Theorem For Secondary Maths Efficiency

Have you ever experienced a situation where you felt that something suddenly starts making sense and you have your own private ‘Eureka’ moment?

Well, the Pythagoras Theorem can be one of those moments.

In many of our secondary maths tuition classes, we have noticed how elated students feel when they at last understand one of the most foundational geometry equations.

In the beginning, they probably take triangles as a confusing shape with too many rules. But once they grasp the Pythagoras Theorem, all the ambiguity starts making sense.

So we thought,

“Why wait for the topic to officially start in the tuition classes? Why not explain everything now?”

A Simple Idea Holding Immense Power In Triangle Geometries

For starters, the theorem is beautifully simple,

a² + b² = c²

In a right-angled triangle, the a and b depict the shorter legs, while c is the hypotenuse or the longest side.

While the formula is simple and easy to memorise, we recommend otherwise. According to our math tutors, the real magic begins when students start seeing how it makes sense, practically.

Let’s visualise this with squares.

Draw a right-angled triangle on a blank sheet.

Now, build squares on each side of the triangle, so that their base touches the side of the triangle.

You’ll notice two things:

• The squares are shorter on the shorter sides of the triangle.
• The square on the hypotenuse is the largest

Now imagine the smaller squares are cut into pieces and placed inside the larger square. You’ll see that they fit perfectly.

Well, you just justified the Pythagoras Theorem, i.e., the sum of the squares of the two shorter sides in a right-angled triangle is equal to the square of the largest side.

Now this equation appears to you as something you can logically explain and not just a formula that someone else has established.

How Important Is The Theorem In Secondary Maths?

This theorem not only comes at all levels of secondary maths but even beyond. As mentioned earlier, it forms the basis of triangle geometries.

And foundations matter, whichever level you are in.

Some everyday applications of the formula include:

• Find the diagonal of a rectangle using the Pythagoras Theorem - Diagonal = √(l² + w²)
• What’s the shortest distance between two points on a graph?

  Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]

• Check if a triangle is right-angled -

  If a² + b² = c², then the triangle is of course right-angled.

Once the students start grasping this, geometry becomes not only an easy mathematics but also an incredibly interesting one.

Some Of The Common Struggles Students Face

In our math tuition classes, we have seen students face confusion regarding the formula when they don't understand it. Many a time, parents approach us and say,

“My child knows the formula but still loses marks in the exams because he doesn’t know how to apply it.”

This is something we hear often. So now we have decided -

Not Anymore!

Our experienced math tutors feel that it’s not exactly about remembering the formula but understanding how to apply it while solving the problems on paper.

Students often:

• Get confused about which side is the hypotenuse
• Overlook the fact that the theorem applies only to right-angled triangles
• Feel panic when the question is worded differently
• Get overwhelmed with real-world contexts, like maps, ladders, graphs, etc.

At Miracle Learning Centre, we devise a constructive approach to remove fears and help them understand smart applications of the theorem.

• We change diagrams, rotate triangles or even hide the right angles during practice sessions.
• We also convert the word problems into visuals for better understanding.

And every time, we ask the students to explain the problem and their understanding of it before trying to solve it. That way, we get to know how well they understand the theorem and its applications and if we need to make it better.

Through constant problem-solving and conceptual explanations, we ensure every student in our maths tuition classes are ‘Right-Angled Triangle experts’ by the time they sit for the exams.

Significance Of Pythagoras Theorem Beyond Exams

Students like anything that they can attach meaning to. In our experience, we have seen that children of this age group don;t like anything abstract or unclear. If you can give them clarity, they will take it along with them beyond the exam papers.

The pythagoras theorem is one such example.

You can use it to explain:

• Why a ladder can lean against a wall easily because of its height
• Why walking diagonally across a park is faster than walking along the two perpendicular sides
• How easily the height or a tree or a building can be calculated without even climbing
• How GPS systems can calculate the shortest distance between two locations

When the students can visualise these real-life examples, application becomes not only easier but also quite intriguing.

Learning Maths As A Fun Subject

Do you wonder how we have managed to stay one of the reputed maths tuition centres in Singapore for so many years?

It’s mostly because we can make maths seem less like a subject and more like ‘fun’ experiments based on sheer logic.

We allow students to ask questions directly, create small interactive groups to solve maths puzzles and discuss theories and theorems in a logical, application-based manner.

As a result, students don’t memorise formulas but learn to understand and have fun with them. If you want your child to have the same fun in mathematics, contact us today. We will ensure that they get over the fear of maths and learn to fall in love with it.