6. Clara claims "all obtuse triangles are similar." Which statement best describes Clara's claim? A. It is true because in every obtuse triangle the sum of two acute angles is less than 90 degrees. O B. It is true because in every obtuse triangle the side between the two acute angles is the longest side. O C.t is false because two obtuse triangles could have sets of angles that are not equal. D. It is false because in two obtuse triangles only the obtuse angles can be congruent.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Question 6

### Similarity of Obtuse Triangles - Educational Discussion

**Question 6: Analyzing Clara's Claim**

Clara claims that "all obtuse triangles are similar." To evaluate Clara's claim, consider the following multiple-choice options:

- **A. It is true because in every obtuse triangle the sum of two acute angles is less than 90 degrees.**
- **B. It is true because in every obtuse triangle the side between the two acute angles is the longest side.**
- **C. It is false because two obtuse triangles could have sets of angles that are not equal.**
- **D. It is false because in two obtuse triangles only the obtuse angles can be congruent.**

### Explanation of the Options:

- **Option A:** This statement is true in general about obtuse triangles, as the sum of the two acute angles is always less than 90 degrees. However, this does not necessarily prove that all obtuse triangles are similar. Similarity of triangles requires all corresponding angles to be equal and the sides to be proportional.

- **Option B:** This describes a property of obtuse triangles (the side between the two acute angles is the longest). However, while correct, it doesn't address the similarity of obtuse triangles directly and comprehensively.

- **Option C:** This option correctly indicates that the sets of angles in two obtuse triangles can differ, meaning the triangles are not necessarily similar. For triangles to be similar, all corresponding angles must be equal.

- **Option D:** This statement also highlights that for two obtuse triangles, only the obtuse angle being congruent is not sufficient for similarity. The other corresponding angles and proportionality of sides are also required for similarity.

Given these considerations, **Option C** is the most accurate choice, explaining why Clara's claim is false based on varying angle measures.
Transcribed Image Text:### Similarity of Obtuse Triangles - Educational Discussion **Question 6: Analyzing Clara's Claim** Clara claims that "all obtuse triangles are similar." To evaluate Clara's claim, consider the following multiple-choice options: - **A. It is true because in every obtuse triangle the sum of two acute angles is less than 90 degrees.** - **B. It is true because in every obtuse triangle the side between the two acute angles is the longest side.** - **C. It is false because two obtuse triangles could have sets of angles that are not equal.** - **D. It is false because in two obtuse triangles only the obtuse angles can be congruent.** ### Explanation of the Options: - **Option A:** This statement is true in general about obtuse triangles, as the sum of the two acute angles is always less than 90 degrees. However, this does not necessarily prove that all obtuse triangles are similar. Similarity of triangles requires all corresponding angles to be equal and the sides to be proportional. - **Option B:** This describes a property of obtuse triangles (the side between the two acute angles is the longest). However, while correct, it doesn't address the similarity of obtuse triangles directly and comprehensively. - **Option C:** This option correctly indicates that the sets of angles in two obtuse triangles can differ, meaning the triangles are not necessarily similar. For triangles to be similar, all corresponding angles must be equal. - **Option D:** This statement also highlights that for two obtuse triangles, only the obtuse angle being congruent is not sufficient for similarity. The other corresponding angles and proportionality of sides are also required for similarity. Given these considerations, **Option C** is the most accurate choice, explaining why Clara's claim is false based on varying angle measures.
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