(11) KESEBANGUNAN PADA SEGITIGA I Cara menentukan panjang sisi dua segitiga yg sebangun MTK IX SMP

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Published on Feb 02, 2025 This response is partially generated with the help of AI. It may contain inaccuracies.

Table of Contents

Introduction

In this tutorial, we will explore how to determine the lengths of sides in two similar triangles, focusing on the principles of triangle similarity. This guide is particularly beneficial for students in middle school mathematics, as it provides a clear method to solve problems involving similar triangles.

Step 1: Understand triangle similarity

  • Triangle similarity means that two triangles have the same shape but different sizes.
  • This occurs when:
    • Their corresponding angles are equal.
    • The lengths of corresponding sides are proportional.

Practical Tip

  • Familiarize yourself with the properties of similar triangles, as this knowledge will be crucial for solving related problems.

Step 2: Identify the corresponding parts of the triangles

  • When solving problems involving similar triangles, identify the following:
    • The pairs of corresponding angles.
    • The lengths of known sides in each triangle.

Example

  • If triangle ABC is similar to triangle DEF, then:
    • Angle A = Angle D
    • Angle B = Angle E
    • Angle C = Angle F
    • Side AB corresponds to side DE, side BC corresponds to side EF, and side AC corresponds to side DF.

Step 3: Set up the proportion

  • Use the lengths of the sides from the similar triangles to create a proportion.

  • The general formula for setting up a proportion is:

    [ \frac{a}{b} = \frac{c}{d} ]

    Where:

    • a and b are the lengths of corresponding sides of the first triangle.
    • c and d are the lengths of corresponding sides of the second triangle.

Practical Tip

  • Make sure to keep the corresponding sides in the correct order to maintain the accuracy of the proportion.

Step 4: Solve for the unknown length

  • Cross-multiply to find the unknown length. For example, if you have:

    [ \frac{5}{10} = \frac{x}{15} ]

    Cross-multiply to get:

    [ 5 \times 15 = 10 \times x ]

    Which simplifies to:

    [ 75 = 10x ]

    Then divide both sides by 10:

    [ x = 7.5 ]

Common Pitfall

  • Ensure that you simplify your equations correctly and double-check your calculations to avoid errors.

Conclusion

In summary, determining the lengths of sides in similar triangles involves understanding their properties, identifying corresponding parts, setting up a proportion, and solving for the unknown length. Practice these steps with various problems to strengthen your understanding of triangle similarity. As you continue learning, consider exploring more complex problems or applications of geometry in real life.