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Which pair of triangles can be proven similar by the SAS- Theorem? AY A P 12 X 15 20 12 R. M A 16

Which pair of triangles can be proven similar by the SAS- Theorem? AY A P 12 X 15 20 12 R. M A 16

Elementary Geometry For College Students, 7e
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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**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
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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