Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
Related questions
Question
![**Similar Triangles by SAS~ Theorem**
**Question:**
Which pair of triangles can be proven similar by the SAS~ Theorem?
**Options:**
**1.**
- **Diagram:**
- Two triangles are shown.
- The first triangle is labeled as \( \triangle ABC \) with vertices \( A, B, \) and \( C \).
- The second triangle is labeled as \( \triangle PQR \) with vertices \( P, Q, \) and \( R \).
**2.**
- **Diagram:**
- Two triangles are shown.
- The first triangle is labeled as \( \triangle ABC \) with vertices \( A, B, \) and \( C \). Sides \( AB \) and \( AC \) are marked with single and double lines respectively, indicating they correspond to sides in another triangle.
- The second triangle is labeled as \( \triangle XYZ \) with vertices \( X, Y, \) and \( Z \). Sides \( XY \) and \( XZ \) are marked with single and double lines respectively, and there is an angle marked between these sides.
**3.**
- **Diagram:**
- Two triangles are shown.
- The first triangle is labeled as \( \triangle ABQ \) with vertices \( A, B, \) and \( Q \). Sides \( AB \) and \( AQ \) are intersected by lines \( BR \) and \( AP \).
- The second triangle is labeled as \( \triangle PRQ \) with vertices \( P, R, \) and \( Q \). Vertices \( P \) and \( R \) are where the triangles intersect, forming angles that can be compared for similarity.
**4.**
- **Diagram:**
- Two right-angled triangles are shown.
- The first triangle is labeled as \( \triangle MNP \) with vertices \( M, N, \) and \( P \). The lengths of the sides are given as \( PM = 9 \), \( MN = 12 \), and \( NP = 15 \).
- The second triangle is labeled as \( \triangle WXL \) with vertices \( W, X, \) and \( L \). The lengths of the sides are given as \( XW = 16 \), \( WL = 12 \), and \( XL = 20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa53c426-a760-4829-b362-653d3877b060%2Fc12031e4-2728-4138-826c-9311c60df5e8%2F21l2bd8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Similar Triangles by SAS~ Theorem**
**Question:**
Which pair of triangles can be proven similar by the SAS~ Theorem?
**Options:**
**1.**
- **Diagram:**
- Two triangles are shown.
- The first triangle is labeled as \( \triangle ABC \) with vertices \( A, B, \) and \( C \).
- The second triangle is labeled as \( \triangle PQR \) with vertices \( P, Q, \) and \( R \).
**2.**
- **Diagram:**
- Two triangles are shown.
- The first triangle is labeled as \( \triangle ABC \) with vertices \( A, B, \) and \( C \). Sides \( AB \) and \( AC \) are marked with single and double lines respectively, indicating they correspond to sides in another triangle.
- The second triangle is labeled as \( \triangle XYZ \) with vertices \( X, Y, \) and \( Z \). Sides \( XY \) and \( XZ \) are marked with single and double lines respectively, and there is an angle marked between these sides.
**3.**
- **Diagram:**
- Two triangles are shown.
- The first triangle is labeled as \( \triangle ABQ \) with vertices \( A, B, \) and \( Q \). Sides \( AB \) and \( AQ \) are intersected by lines \( BR \) and \( AP \).
- The second triangle is labeled as \( \triangle PRQ \) with vertices \( P, R, \) and \( Q \). Vertices \( P \) and \( R \) are where the triangles intersect, forming angles that can be compared for similarity.
**4.**
- **Diagram:**
- Two right-angled triangles are shown.
- The first triangle is labeled as \( \triangle MNP \) with vertices \( M, N, \) and \( P \). The lengths of the sides are given as \( PM = 9 \), \( MN = 12 \), and \( NP = 15 \).
- The second triangle is labeled as \( \triangle WXL \) with vertices \( W, X, \) and \( L \). The lengths of the sides are given as \( XW = 16 \), \( WL = 12 \), and \( XL = 20
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