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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Question
![**Question:**
1. Which two triangles are congruent by ASA? Explain.
**Diagram Explanation:**
The image shows two triangles:
- Triangle SVT
- Angle S, marked with an arc
- Angle V, marked with a double arc
- Side VT has a notch indicating it's equal to side XY
- Triangle RXY
- Angle R, marked with an arc
- Angle X, marked with a double arc
In both triangles:
- Angle R (in triangle RXY) is congruent to Angle S (in triangle SVT).
- Angle X (in triangle RXY) is congruent to Angle V (in triangle SVT).
- The side VT in triangle SVT is congruent to side XY in triangle RXY, as indicated by the marks.
This demonstrates that these triangles are congruent by the Angle-Side-Angle (ASA) postulate because two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9002a4f7-5f5e-4095-914d-674667d92904%2F34ad09aa-3d7d-4727-aef4-0eb360cfa1ba%2F6s1dnoc_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
1. Which two triangles are congruent by ASA? Explain.
**Diagram Explanation:**
The image shows two triangles:
- Triangle SVT
- Angle S, marked with an arc
- Angle V, marked with a double arc
- Side VT has a notch indicating it's equal to side XY
- Triangle RXY
- Angle R, marked with an arc
- Angle X, marked with a double arc
In both triangles:
- Angle R (in triangle RXY) is congruent to Angle S (in triangle SVT).
- Angle X (in triangle RXY) is congruent to Angle V (in triangle SVT).
- The side VT in triangle SVT is congruent to side XY in triangle RXY, as indicated by the marks.
This demonstrates that these triangles are congruent by the Angle-Side-Angle (ASA) postulate because two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.
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