To solve the problem, we use the Midpoint Theorem in geometry, which states:

"The line segment joining the midpoints of two sides of a triangle is parallel to the third side and its length is half the length of the third side."

Here is the step-by-step solution:

Step 1: Identify the midpoints

• $D$ is the midpoint of $AB$.
• $E$ is the midpoint of $AC$.

Step 2: Apply the Midpoint Theorem

• According to the Midpoint Theorem, the line segment $DE$:
  1. Is parallel to $BC$ ($DE \parallel BC$).
  2. Has a length that is half the length of $BC$.

Step 3: Calculate the length of $DE$

• The length of $BC$ is given as $6 \, \text{cm}$.
• Therefore, the length of $DE$ is: $DE = \frac{1}{2} \times BC = \frac{1}{2} \times 6 = 3 \, \text{cm}.$

Final Answer:

The length of $DE$ is: $\boxed{3 \, \text{cm}}$

Would you like further details on this theorem or its applications?

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Here are 5 related questions to explore:

1. What is the Midpoint Theorem, and how can it be proved?
2. If $BC = 10 \, \text{cm}$, what would be the length of $DE$?
3. How does the Midpoint Theorem relate to coordinate geometry?
4. What are some practical applications of the Midpoint Theorem in real-world problems?
5. How do we verify $DE \parallel BC$ in this problem?

Tip: In problems involving midpoints and parallel lines, the Midpoint Theorem is a powerful and straightforward tool for solving geometry problems.