https://file.aiquickdraw.com/mathbot/file/1726625222734nu10yb0l.jpg

The problem shows two similar triangles, \( \triangle ABC \) and \( \triangle DEF \). Since the triangles are similar, the corresponding sides of the triangles are proportional.

- For \( \triangle ABC \), the sides are:
  - \( AB = 6 \) inches
  - \( BC = 7 \) inches
  - \( AC \) is not given

- For \( \triangle DEF \), the sides are:
  - \( DE = 4 \) inches
  - \( DF = x \) inches
  - \( EF \) is not given

To find which proportion is correct, we need to set up ratios of corresponding sides:

- \( AB \) corresponds to \( DE \)
- \( BC \) corresponds to \( DF \)

So, the correct proportion would be:

\[
\frac{AB}{DE} = \frac{BC}{DF}
\]

Substituting the known values:

\[
\frac{6}{4} = \frac{7}{x}
\]

This matches option **D**: 

\[
\frac{4}{x} = \frac{7}{6}
\]

The equation can be rearranged to:

\[
\frac{6}{4} = \frac{7}{x}
\]

So the correct answer is **D**.

Would you like further clarification or details on the steps? Here are some follow-up questions to deepen your understanding:

1. What are corresponding sides in similar triangles?
2. How can you solve proportions like \( \frac{6}{4} = \frac{7}{x} \)?
3. What does it mean for two triangles to be similar?
4. How would the solution change if different sides were involved?
5. How can we apply the cross-multiplication method to solve for \( x \)?

**Tip**: Always ensure that corresponding sides are matched correctly when setting up proportions for similar triangles!

Which proportion must be true? Triangle ABC and Triangle DEF are similar. Given AB = 6 in, BC = 7 in, DE = 4 in, DF = x in, and the proportion options A, B, C, D.

Explore how to solve proportions for two similar triangles ABC and DEF. Learn the key concepts of triangle similarity and proportional sides with an example where AB = 6 in, BC = 7 in, DE = 4 in, and DF = x in. Find out which proportion holds true using the similarity theorem. Suitable for Grade 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation