TEOREMA PYTHAGORAS. Materi Soal dan pembahasan

Introduction

This tutorial focuses on understanding the Pythagorean Theorem, a fundamental principle in geometry that relates the lengths of the sides of a right triangle. We'll break down the theorem, explore its applications, and solve practical problems step-by-step.

Step 1: Understand the Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed with the formula:

a² + b² = c²

Where:

• c is the length of the hypotenuse
• a and b are the lengths of the other two sides

Practical Advice

• Familiarize yourself with identifying right triangles in different contexts.
• Remember that the theorem only applies to right triangles.

Step 2: Identify the Sides of a Right Triangle

When working on problems involving the Pythagorean Theorem, it's crucial to correctly identify which sides correspond to a, b, and c.

How to Identify

1. Look for the right angle in the triangle (often marked with a small square).
2. Identify the hypotenuse (the longest side).
3. The other two sides will be a and b.

Practical Advice

• Use a ruler or a protractor if you're drawing your triangle to ensure accuracy.

Step 3: Apply the Theorem to Solve Problems

To solve for the unknown side of a right triangle using the theorem, follow these steps:

1. Determine which side you need to find.
2. Rearrange the formula based on the known sides:
   • If finding c (hypotenuse):

     c = √(a² + b²)
     

   • If finding a:

     a = √(c² - b²)
     

   • If finding b:

     b = √(c² - a²)
     

Example Problem

Given a triangle where a = 3 and b = 4, find c:

1. Substitute into the formula:

   c = √(3² + 4²)
   

2. Calculate:

   c = √(9 + 16) = √25 = 5
   

Common Pitfalls

• Ensure all measurements are in the same units.
• Double-check calculations to avoid simple arithmetic mistakes.

Step 4: Explore Real-World Applications

The Pythagorean Theorem is used in various fields such as construction, navigation, and computer graphics. Here’s how you can apply it:

• Construction: Ensure structures are built at right angles by measuring diagonal distances.
• Navigation: Calculate the shortest path between two points in a coordinate system.
• Design: Create accurate layouts and dimensions in graphic design.

Conclusion

The Pythagorean Theorem is a powerful tool in geometry that has practical applications in everyday life. By understanding its principles and practicing problem-solving techniques, you can confidently apply this theorem in various situations. To further your knowledge, practice with different triangle problems and explore more complex applications in real-world scenarios.