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**Question 13** What congruency theorem would be applied? **Given:** - ∠X ≅ ∠Z - XY ≅ ZY **Prove:** - AZ ≅ BX The image depicts a geometric diagram with points X, Y, Z, A, and B. The lines and angles are labeled accordingly. Below is the description of the elements in the diagram: 1. **Points and Lines:** - Points X, Y, and Z form a triangle. - Point A is on line segment XY. - Point B is on line segment YZ. - Lines XA and BZ are drawn across the triangle, intersecting at point A and B respectively. 2. **Congruencies Given:** - Angle X is congruent to Angle Z (∠X ≅ ∠Z). - Line segment XY is congruent to line segment ZY (XY ≅ ZY). 3. **To Prove:** - Line segment AZ is congruent to line segment BX (AZ ≅ BX). The question asks for the application of a congruency theorem to establish the relationship between segments AZ and BX based on the given information.

**Question 13** What congruency theorem would be applied? **Given:** - ∠X ≅ ∠Z - XY ≅ ZY **Prove:** - AZ ≅ BX The image depicts a geometric diagram with points X, Y, Z, A, and B. The lines and angles are labeled accordingly. Below is the description of the elements in the diagram: 1. **Points and Lines:** - Points X, Y, and Z form a triangle. - Point A is on line segment XY. - Point B is on line segment YZ. - Lines XA and BZ are drawn across the triangle, intersecting at point A and B respectively. 2. **Congruencies Given:** - Angle X is congruent to Angle Z (∠X ≅ ∠Z). - Line segment XY is congruent to line segment ZY (XY ≅ ZY). 3. **To Prove:** - Line segment AZ is congruent to line segment BX (AZ ≅ BX). The question asks for the application of a congruency theorem to establish the relationship between segments AZ and BX based on the given information.

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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**Question 13** What congruency theorem would be applied? **Given:** - ∠X ≅ ∠Z - XY ≅ ZY **Prove:** - AZ ≅ BX The image depicts a geometric diagram with points X, Y, Z, A, and B. The lines and angles are labeled accordingly. Below is the description of the elements in the diagram: 1. **Points and Lines:** - Points X, Y, and Z form a triangle. - Point A is on line segment XY. - Point B is on line segment YZ. - Lines XA and BZ are drawn across the triangle, intersecting at point A and B respectively. 2. **Congruencies Given:** - Angle X is congruent to Angle Z (∠X ≅ ∠Z). - Line segment XY is congruent to line segment ZY (XY ≅ ZY). 3. **To Prove:** - Line segment AZ is congruent to line segment BX (AZ ≅ BX). The question asks for the application of a congruency theorem to establish the relationship between segments AZ and BX based on the given information.
Transcribed Image Text:**Question 13** What congruency theorem would be applied? **Given:** - ∠X ≅ ∠Z - XY ≅ ZY **Prove:** - AZ ≅ BX The image depicts a geometric diagram with points X, Y, Z, A, and B. The lines and angles are labeled accordingly. Below is the description of the elements in the diagram: 1. **Points and Lines:** - Points X, Y, and Z form a triangle. - Point A is on line segment XY. - Point B is on line segment YZ. - Lines XA and BZ are drawn across the triangle, intersecting at point A and B respectively. 2. **Congruencies Given:** - Angle X is congruent to Angle Z (∠X ≅ ∠Z). - Line segment XY is congruent to line segment ZY (XY ≅ ZY). 3. **To Prove:** - Line segment AZ is congruent to line segment BX (AZ ≅ BX). The question asks for the application of a congruency theorem to establish the relationship between segments AZ and BX based on the given information.
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