https://file.aiquickdraw.com/mathbot/file/1729763759950tp1oqiu5.jpg

This problem involves two parallel segments, \( FG \parallel IJ \), and you are asked to find the length of \( IJ \), given the following information:

- \( HF = 30 \)
- \( HI = 9 \)
- \( FG = 40 \)

Since the lines are parallel, we can use the concept of similar triangles. Triangles \( \triangle FGH \) and \( \triangle IJH \) are similar by the Basic Proportionality Theorem (also called Thales' Theorem) because \( FG \parallel IJ \).

The sides of the triangles will be proportional, so the ratio of the corresponding sides is:

\[
\frac{IJ}{FG} = \frac{HI}{HF}
\]

We can plug in the given values:

\[
\frac{IJ}{40} = \frac{9}{30}
\]

Now, solve for \( IJ \):

\[
IJ = 40 \times \frac{9}{30}
\]

\[
IJ = 40 \times \frac{3}{10} = 12
\]

Thus, the length of \( IJ \) is 12 units.

Would you like more details or have any questions? Here are some related questions:

1. How are similar triangles identified in a problem?
2. What is the Basic Proportionality Theorem?
3. Can this problem be solved using a different method?
4. How can the concept of ratios help in geometry problems?
5. What are other properties of parallel lines in triangles?

**Tip:** Always look for parallel lines in triangles, as they often indicate similar triangles and proportionality.

In triangle FGH, FG is parallel to IJ. Given that HF = 30, HI = 9, and FG = 40, find IJ.

Solve a geometry problem involving similar triangles and proportionality: given HF = 30, HI = 9, and FG = 40, find the length of IJ using the Basic Proportionality Theorem. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation