https://file.aiquickdraw.com/mathbot/file/17271887281543hn7kt6w.jpg

The diagram provides the following information:

- \( AB \cong CD \) (i.e., the length of \( AB \) is equal to the length of \( CD \)).
- \( CD \cong BC \) (i.e., the length of \( CD \) is equal to the length of \( BC \)).

From the diagram, the lengths of the segments are expressed as:
- \( AB = 2x + 4 \),
- \( CD = 10 - x \),
- \( BC = BC \) (we are solving for \( BC \)).

Since \( AB = CD \), we can set up an equation:

\[
2x + 4 = 10 - x.
\]

Let's solve for \( x \).

\[
2x + x = 10 - 4,
\]
\[
3x = 6,
\]
\[
x = 2.
\]

Now, we substitute \( x = 2 \) back into the expression for \( BC \), using the fact that \( BC = CD \). Since \( CD = 10 - x \), we get:

\[
BC = 10 - 2 = 8.
\]

Thus, the length of \( BC \) is \( \boxed{8} \).

Would you like any further details, or have any questions?

### Related questions:
1. What are the properties of congruent segments?
2. How can we use algebra to solve geometric problems?
3. What is the significance of setting two segment expressions equal to each other?
4. How would the problem change if \( AB \) and \( CD \) were not congruent?
5. How do we check if our solution is correct?

**Tip:** Always substitute your solution back into the original equation to verify it.

In the diagram, AB ≅ CD and CD ≅ BC. Find BC.

Learn how to solve for the length of segment BC using algebra and properties of congruent segments. In this problem, AB ≅ CD and CD ≅ BC. A step-by-step solution is provided for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation