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elow. 7 Z

elow. 7 Z

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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24. consider RST and XYZ shown below. Which postulate or theorem proves that the triangles are congruent 

**Question 24: Congruence of Triangles** Consider ∆RST and ∆XYZ shown below. Two triangles are depicted: 1. Triangle RST: - Angle at vertex S is 48° - Side RS = 7 units - Side RT = 3 units 2. Triangle XYZ: - Angle at vertex Y is 48° - Side XY = 7 units - Side YZ = 3 units **Which postulate or theorem proves that the triangles are congruent?** - **A. SSS** - **B. SSA** - **C. SAS** - **D. ASA** *Note:* The postulates or theorems used to prove congruence between triangles include: - **SSS (Side-Side-Side):** All three corresponding sides are equal. - **SAS (Side-Angle-Side):** Two corresponding sides and the included angle are equal. - **ASA (Angle-Side-Angle):** Two corresponding angles and the included side are equal. - **SSA (Side-Side-Angle):** Generally does not prove congruence unless specific conditions are met. *Detailed Explanation of Diagrams:* - The triangles have one side measuring 7 units and another side measuring 3 units. - Both triangles have one angle measuring 48°. - The orientation and labeling of vertices correspond in such a way that it suggests using the corresponding sides and included angle for congruence determination. **Powered by LinkIt!**
Transcribed Image Text:**Question 24: Congruence of Triangles** Consider ∆RST and ∆XYZ shown below. Two triangles are depicted: 1. Triangle RST: - Angle at vertex S is 48° - Side RS = 7 units - Side RT = 3 units 2. Triangle XYZ: - Angle at vertex Y is 48° - Side XY = 7 units - Side YZ = 3 units **Which postulate or theorem proves that the triangles are congruent?** - **A. SSS** - **B. SSA** - **C. SAS** - **D. ASA** *Note:* The postulates or theorems used to prove congruence between triangles include: - **SSS (Side-Side-Side):** All three corresponding sides are equal. - **SAS (Side-Angle-Side):** Two corresponding sides and the included angle are equal. - **ASA (Angle-Side-Angle):** Two corresponding angles and the included side are equal. - **SSA (Side-Side-Angle):** Generally does not prove congruence unless specific conditions are met. *Detailed Explanation of Diagrams:* - The triangles have one side measuring 7 units and another side measuring 3 units. - Both triangles have one angle measuring 48°. - The orientation and labeling of vertices correspond in such a way that it suggests using the corresponding sides and included angle for congruence determination. **Powered by LinkIt!**
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