If `Delta ABC ~ Delta DEF and AB = DE, BC = 8 cm,` then the value of EF ?

Answer

To solve the problem, we need to use the properties of similar triangles. Given that triangle ABC is similar to triangle DEF, we know that the corresponding sides of these triangles are in proportion.

### Step-by-Step Solution:

1. **Identify the Corresponding Sides**:
Since triangle ABC is similar to triangle DEF, the corresponding sides are:
- AB corresponds to DE
- BC corresponds to EF

2. **Set Up the Proportion**:
From the similarity of the triangles, we can set up the following proportion:
\[ \frac{AB}{DE} = \frac{BC}{EF} \]

3. **Substitute the Known Values**:
We know that:
- \( AB = DE \) (given)
- \( BC = 8 \, \text{cm} \) (given)
- Let \( EF \) be the unknown we want to find.

Substituting these values into the proportion gives:
\[ \frac{AB}{AB} = \frac{8}{EF} \]

4. **Simplify the Proportion**:
Since \( \frac{AB}{AB} = 1 \), we can simplify the equation to:
\[ 1 = \frac{8}{EF} \]

5. **Cross Multiply to Solve for EF**:
Cross multiplying gives:
\[ EF = 8 \]

### Final Answer:
Thus, the value of \( EF \) is \( 8 \, \text{cm} \).

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