### Similarity of Triangles using SAS Similarity In the diagram below, \( \triangle ABC \sim \triangle DEF \).  #### Diagram Explanation: - The triangle \( \triangle ABC \) has vertices A, B, and C, with side lengths: - \( AB = 6 \) - \( AC = 8 \) - \( BC \) (unknown) - The triangle \( \triangle DEF \) has vertices D, E, and F, with unknown side lengths. ### Given Information: \( AB = 6 \) and \( AC = 8 \). #### Question: Which statement will justify similarity by SAS (Side-Angle-Side) Similarity? #### Options: 1. \( DE = 9 \), \( DF = 12 \), and \( \angle A \cong \angle D \) 2. \( DE = 36 \), \( DF = 64 \), and \( \angle C \cong \angle F \) 3. \( DE = 8 \), \( DF = 10 \), and \( \angle A \cong \angle D \) 4. \( DE = 15 \), \( DF = 20 \), and \( \angle C \cong \angle F \) #### Multiple Choice Answers: - O A - O B - O C - O D In SAS similarity, two triangles are similar if two sides and the included angle of one triangle are proportional to the corresponding two sides and the included angle of another triangle. To verify the similarity, confirm that: \[ \frac{AB}{DE} = \frac{AC}{DF} \] and the included angle (\( \angle A \) or \( \angle C \)) matches. Review the provided statements and confirm which one holds the similarity criterion to determine the correct answer.
### Similarity of Triangles using SAS Similarity In the diagram below, \( \triangle ABC \sim \triangle DEF \).  #### Diagram Explanation: - The triangle \( \triangle ABC \) has vertices A, B, and C, with side lengths: - \( AB = 6 \) - \( AC = 8 \) - \( BC \) (unknown) - The triangle \( \triangle DEF \) has vertices D, E, and F, with unknown side lengths. ### Given Information: \( AB = 6 \) and \( AC = 8 \). #### Question: Which statement will justify similarity by SAS (Side-Angle-Side) Similarity? #### Options: 1. \( DE = 9 \), \( DF = 12 \), and \( \angle A \cong \angle D \) 2. \( DE = 36 \), \( DF = 64 \), and \( \angle C \cong \angle F \) 3. \( DE = 8 \), \( DF = 10 \), and \( \angle A \cong \angle D \) 4. \( DE = 15 \), \( DF = 20 \), and \( \angle C \cong \angle F \) #### Multiple Choice Answers: - O A - O B - O C - O D In SAS similarity, two triangles are similar if two sides and the included angle of one triangle are proportional to the corresponding two sides and the included angle of another triangle. To verify the similarity, confirm that: \[ \frac{AB}{DE} = \frac{AC}{DF} \] and the included angle (\( \angle A \) or \( \angle C \)) matches. Review the provided statements and confirm which one holds the similarity criterion to determine the correct answer.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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#### Diagram Explanation:
- The triangle \( \triangle ABC \) has vertices A, B, and C, with side lengths:
- \( AB = 6 \)
- \( AC = 8 \)
- \( BC \) (unknown)
- The triangle \( \triangle DEF \) has vertices D, E, and F, with unknown side lengths.
### Given Information:
\( AB = 6 \) and \( AC = 8 \).
#### Question:
Which statement will justify similarity by SAS (Side-Angle-Side) Similarity?
#### Options:
1. \( DE = 9 \), \( DF = 12 \), and \( \angle A \cong \angle D \)
2. \( DE = 36 \), \( DF = 64 \), and \( \angle C \cong \angle F \)
3. \( DE = 8 \), \( DF = 10 \), and \( \angle A \cong \angle D \)
4. \( DE = 15 \), \( DF = 20 \), and \( \angle C \cong \angle F \)
#### Multiple Choice Answers:
- O A
- O B
- O C
- O D
In SAS similarity, two triangles are similar if two sides and the included angle of one triangle are proportional to the corresponding two sides and the included angle of another triangle. To verify the similarity, confirm that:
\[ \frac{AB}{DE} = \frac{AC}{DF} \]
and the included angle (\( \angle A \) or \( \angle C \)) matches.
Review the provided statements and confirm which one holds the similarity criterion to determine the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F492f8302-2af6-4a90-9bdc-ae62d55032ea%2Fad5be4c3-4655-49ca-871d-550406aa6263%2Fagre3s.jpeg&w=3840&q=75)
Transcribed Image Text:### Similarity of Triangles using SAS Similarity
In the diagram below, \( \triangle ABC \sim \triangle DEF \).
#### Diagram Explanation:
- The triangle \( \triangle ABC \) has vertices A, B, and C, with side lengths:
- \( AB = 6 \)
- \( AC = 8 \)
- \( BC \) (unknown)
- The triangle \( \triangle DEF \) has vertices D, E, and F, with unknown side lengths.
### Given Information:
\( AB = 6 \) and \( AC = 8 \).
#### Question:
Which statement will justify similarity by SAS (Side-Angle-Side) Similarity?
#### Options:
1. \( DE = 9 \), \( DF = 12 \), and \( \angle A \cong \angle D \)
2. \( DE = 36 \), \( DF = 64 \), and \( \angle C \cong \angle F \)
3. \( DE = 8 \), \( DF = 10 \), and \( \angle A \cong \angle D \)
4. \( DE = 15 \), \( DF = 20 \), and \( \angle C \cong \angle F \)
#### Multiple Choice Answers:
- O A
- O B
- O C
- O D
In SAS similarity, two triangles are similar if two sides and the included angle of one triangle are proportional to the corresponding two sides and the included angle of another triangle. To verify the similarity, confirm that:
\[ \frac{AB}{DE} = \frac{AC}{DF} \]
and the included angle (\( \angle A \) or \( \angle C \)) matches.
Review the provided statements and confirm which one holds the similarity criterion to determine the correct answer.
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