Teorema Pythagoras [Part 4] - Menentukan Perbandingan Sisi Segitiga Siku-siku

Introduction

In this tutorial, we will explore the Pythagorean Theorem, specifically focusing on how to determine the ratio of the sides of a right triangle. This guide is particularly useful for eighth-grade students studying geometry and will help you understand the practical applications of the theorem, especially in the context of distance learning.

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 mathematically as:

c^2 = a^2 + b^2

Where:

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

Practical Tip

• Always remember to ensure that you are dealing with a right triangle before applying this theorem.

Step 2: Identify the Sides of the Triangle

When given a right triangle, identify and label the sides.

• Hypotenuse (c): The longest side, opposite the right angle.
• Legs (a and b): The two shorter sides that form the right angle.

Common Pitfalls to Avoid

• Confusing the hypotenuse with one of the legs.
• Mislabeling the sides, especially in more complex diagrams.

Step 3: Calculate the Lengths of the Sides

To find the lengths of the sides of a right triangle using the Pythagorean Theorem, follow these steps:

1. If you know the lengths of two sides, substitute them into the formula:

   • For example, if a = 3 cm and b = 4 cm:

     c^2 = (3)^2 + (4)^2
     c^2 = 9 + 16
     c^2 = 25
     c = 5 cm
     

2. If you only know one side and the hypotenuse, rearrange the formula to solve for the unknown side:

   • If c = 5 cm and a = 3 cm:

     b^2 = c^2 - a^2
     b^2 = (5)^2 - (3)^2
     b^2 = 25 - 9
     b^2 = 16
     b = 4 cm
     

Step 4: Determine the Ratio of the Sides

Once you have the lengths of the sides, you can determine the ratio.

1. Calculate the ratio using the lengths:

   • For example, if a = 3 cm and b = 4 cm, the ratio of the sides can be expressed as:

     Ratio = a : b = 3 : 4
     

2. Simplify the ratio if possible.

Practical Tip

• Ratios can help in understanding the relationship between the sides and are useful in similar triangles.

Step 5: Calculate the Area of a Rectangle Formed by the Triangle

If you have a specific triangle configuration, such as points forming a rectangle, you can calculate the area by multiplying the lengths of the sides:

• For example, if KL = 3.5 cm and KN = 3.5√3 cm, the area (A) is calculated as follows:

  A = KL * KN
  A = 3.5 cm * 3.5√3 cm
  A = 12.25√3 cm²
  

Conclusion

Understanding the Pythagorean Theorem and the relationships between the sides of a right triangle is essential in geometry. By following the steps outlined in this tutorial, you can confidently calculate side lengths, determine ratios, and even find areas of related shapes. Practice these concepts with different triangle configurations to solidify your understanding. Keep studying and apply these principles in real-world scenarios!