Angelo has a triangle for an art project labeled IGH. He reduced the size of the triangle by a factor of 5 to fit a smaller frame and labeled that similar triangle DFE.


Select the correct similarity statement about these triangles.


To determine the correct similarity statement for the triangles \( \triangle IGH \) and \( \triangle DFE \), we need to establish the relationship between their corresponding sides and angles based on the given information.

Given:
- \( \triangle IGH \) is reduced by a factor of 5 to form \( \triangle DFE \).
- The triangles are similar by the definition of the reduction (scaling).

### Similarity Statement

When a triangle is reduced by a factor, each side length of the smaller triangle is a certain fraction (in this case, \(\frac{1}{5}\)) of the corresponding side length of the original triangle. The corresponding angles in similar triangles remain the same, but the side lengths are proportional.

For the similarity statement, we need to correctly match the vertices of the triangles so that the order of the vertices reflects the corresponding angles.

1. \( \triangle IGH \) corresponds to \( \triangle DFE \).
2. The side lengths are reduced by a factor of 5.

### Notation for Similar Triangles

The correct notation for similar triangles uses the \(\sim\) symbol and lists corresponding vertices in order:

\[ \triangle IGH \sim \triangle DFE \]

This notation indicates that:
- \( \angle I \) corresponds to \( \angle D \)
- \( \angle G \) corresponds to \( \angle F \)
- \( \angle H \) corresponds to \( \angle E \)

### Conclusion

The correct similarity statement is:

\[ \triangle IGH \sim \triangle DFE \]

This notation confirms that the triangles are similar and lists the vertices in corresponding order.

Do you want any details or have any questions?

---

**Relative Questions:**

1. What does it mean for two triangles to be similar?
2. How do you determine the scale factor between two similar triangles?
3. What are the properties of similar triangles?
4. How can you verify that two triangles are similar by using their sides and angles?
5. What are some common applications of similar triangles in real life?
6. How does the reduction or enlargement of a triangle affect its area?
7. What is the significance of corresponding angles in similar triangles?
8. How can we use similarity to solve problems involving triangles in geometry?

**Tip:** When working with similar triangles, always remember that corresponding angles are equal and corresponding sides are proportional. This helps in identifying and solving problems related to similar figures.

Explore the similarity between triangles IGH and DFE, where triangle IGH is reduced by a factor of 5 to form triangle DFE. Learn how corresponding angles and sides are proportional in similar triangles. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation