Triangle ABC is similar to triangle EFD. What scale factor is required to dilate triangle ABC so that its image, A’B’C’, is congruent to triangle EFD? ### Triangle Similarity ProblemIn the given problem, triangle $ \triangle ABC $ is similar to triangle $ \triangle DEF $. We are required to find the ratio of the sides AB to DE.#### Diagrams:**Triangle $ \triangle ABC $**:- Vertices: $ A, B, C $- Side lengths: - $ AB = 12 $ - $ AC = 15 $ - $ BC $ is not provided**Triangle $ \triangle DEF $**:- Vertices: $ D, E, F $- Side lengths: - $ DE = 3 $ - $ EF = 5 $ - $ DF $ is not provided**Given Similarity Condition:**- $ \triangle ABC $ ∼ $ \triangle DEF $### Objective:Calculate the ratio of the corresponding sides $ AB $ and $ DE $.### Multiple Choice Options:- A) $ 3 $- B) $ \frac{5}{12} $- C) $ \frac{1}{3} $- D) $ \frac{12}{5} $**Solution Steps:**Since the triangles are similar, the ratio of their corresponding sides must be equal. Therefore, we set up the ratio of side $ AB $ to side $ DE $:\[ \frac{AB}{DE} = \frac{12}{3} = 4 \]However, the given options might have a typographical error as the values do not match directly. Review carefully:**Interpretation:**If there is an intended simplification error:- Verify the ratios.- Correctly simplified, the intended ratio might mean 4 could have been overlooked.Select the closest logical answer reflecting the understanding:Consider simplified values among given:**Correct Answer:**None given directly reflect above; logical inference contextually needed. Revisit problem constraints if error exists.---End educational content analysis. Ensure revisiting parameters if mismatch persists.

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Answered: Triangle ABC is similar to triangle…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Triangle ABC is similar to triangle EFD. What scale factor is required to dilate triangle ABC so that its image, A’B’C’, is congruent to triangle EFD?

### Triangle Similarity Problem

In the given problem, triangle $ \triangle ABC $ is similar to triangle $ \triangle DEF $. We are required to find the ratio of the sides AB to DE.

#### Diagrams:

**Triangle $ \triangle ABC $**:
- Vertices: $ A, B, C $
- Side lengths:
- $ AB = 12 $
- $ AC = 15 $
- $ BC $ is not provided

**Triangle $ \triangle DEF $**:
- Vertices: $ D, E, F $
- Side lengths:
- $ DE = 3 $
- $ EF = 5 $
- $ DF $ is not provided

**Given Similarity Condition:**
- $ \triangle ABC $ ∼ $ \triangle DEF $

### Objective:

Calculate the ratio of the corresponding sides $ AB $ and $ DE $.

### Multiple Choice Options:

- A) $ 3 $

- B) $ \frac{5}{12} $

- C) $ \frac{1}{3} $

- D) $ \frac{12}{5} $

**Solution Steps:**

Since the triangles are similar, the ratio of their corresponding sides must be equal. Therefore, we set up the ratio of side $ AB $ to side $ DE $:

\[ \frac{AB}{DE} = \frac{12}{3} = 4 \]

However, the given options might have a typographical error as the values do not match directly. Review carefully:

**Interpretation:**

If there is an intended simplification error:

- Verify the ratios.
- Correctly simplified, the intended ratio might mean 4 could have been overlooked.

Select the closest logical answer reflecting the understanding:

Consider simplified values among given:

**Correct Answer:**
None given directly reflect above; logical inference contextually needed. Revisit problem constraints if error exists.

---

End educational content analysis. Ensure revisiting parameters if mismatch persists.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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