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Complete the proof that ATUY ≈ AWXV. T 1 2 4 5 3 ZUTY ZVWX 6 7 Statement 8 X XY UV ZTYUZWVX UY = XY + UX VX UV + UX UY = UV + UX VX = UY ATUY AWXV U W Reason Given Angles forming a linear pair sum to 180° ASA Corresponding Angles Theorem CPCTC Definition of angle bisector Definition of congruence ><

Complete the proof that ATUY ≈ AWXV. T 1 2 4 5 3 ZUTY ZVWX 6 7 Statement 8 X XY UV ZTYUZWVX UY = XY + UX VX UV + UX UY = UV + UX VX = UY ATUY AWXV U W Reason Given Angles forming a linear pair sum to 180° ASA Corresponding Angles Theorem CPCTC Definition of angle bisector Definition of congruence ><

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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The image presents a geometric proof showing that triangles \( \triangle TUY \cong \triangle WXV \). ### Diagram Explanation - There are two triangles, \( \triangle TUY \) and \( \triangle WXV \), with corresponding marked angles and sides. - Angles at \( T \) and \( W \), and angles at \( U \) and \( V \) have identical marking, suggesting they are equal. - Line segments \( XY \) and \( UV \) are indicated as equal by notation. ### Proof Table **Statement** | **Reason** --- | --- 1. \( XY = UV \) | Given 2. | Angles forming a linear pair sum to 180° 3. \( \angle TUY \cong \angle WVX \) | ASA (Angle-Side-Angle) 4. \( UY = XY + UX \) | CPCTC (Corresponding Parts of Congruent Triangles are Congruent) 5. \( VX = UV + UX \) | Definition of angle bisector 6. \( UY = UV + UX \) | Definition of congruence 7. \( VX = UY \) | 8. \( \triangle TUY \cong \triangle WXV \) | The proof employs the Angle-Side-Angle (ASA) criterion for triangle congruence, relying on angle correspondence and equal line segment pairings.
Transcribed Image Text:The image presents a geometric proof showing that triangles \( \triangle TUY \cong \triangle WXV \). ### Diagram Explanation - There are two triangles, \( \triangle TUY \) and \( \triangle WXV \), with corresponding marked angles and sides. - Angles at \( T \) and \( W \), and angles at \( U \) and \( V \) have identical marking, suggesting they are equal. - Line segments \( XY \) and \( UV \) are indicated as equal by notation. ### Proof Table **Statement** | **Reason** --- | --- 1. \( XY = UV \) | Given 2. | Angles forming a linear pair sum to 180° 3. \( \angle TUY \cong \angle WVX \) | ASA (Angle-Side-Angle) 4. \( UY = XY + UX \) | CPCTC (Corresponding Parts of Congruent Triangles are Congruent) 5. \( VX = UV + UX \) | Definition of angle bisector 6. \( UY = UV + UX \) | Definition of congruence 7. \( VX = UY \) | 8. \( \triangle TUY \cong \triangle WXV \) | The proof employs the Angle-Side-Angle (ASA) criterion for triangle congruence, relying on angle correspondence and equal line segment pairings.
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