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In AAGE and AOLD, ZGAE = ZLOD, and AE OD. To prove that AAGE and AOLD are congruent by SAS, what other information is needed?

In AAGE and AOLD, ZGAE = ZLOD, and AE OD. To prove that AAGE and AOLD are congruent by SAS, what other information is needed?

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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**Title: Understanding Congruency Through SAS** **Problem Statement:** In triangles \( \triangle AGE \) and \( \triangle OLD \), it is given that: - \( \angle GAE \cong \angle LOD \) - \( AE \cong OD \) To prove that \( \triangle AGE \cong \triangle OLD \) by the Side-Angle-Side (SAS) congruence theorem, what other information is needed? **Options:** - F: \( GE \cong LD \) - G: \( AG \cong OL \) - H: \( \angle AGE \cong \angle OLD \) - J: \( \angle AEG \cong \angle ODL \) **Explanation:** To apply the SAS congruence theorem, two sides and the angle between them must be congruent. Given \( AE \cong OD \) and \( \angle GAE \cong \angle LOD \), we need one more pair of corresponding sides to be congruent. **Diagrams:** No diagrams or graphs accompany the text. The problem requires identifying the missing piece of information that would complete the SAS criteria for proving triangle congruence. The choices involve various side or angle congruences. Remember, SAS means two sides and the included angle are congruent between two triangles. **Conclusion:** Select the correct option to demonstrate understanding of the SAS criterion for triangle congruency.
Transcribed Image Text:**Title: Understanding Congruency Through SAS** **Problem Statement:** In triangles \( \triangle AGE \) and \( \triangle OLD \), it is given that: - \( \angle GAE \cong \angle LOD \) - \( AE \cong OD \) To prove that \( \triangle AGE \cong \triangle OLD \) by the Side-Angle-Side (SAS) congruence theorem, what other information is needed? **Options:** - F: \( GE \cong LD \) - G: \( AG \cong OL \) - H: \( \angle AGE \cong \angle OLD \) - J: \( \angle AEG \cong \angle ODL \) **Explanation:** To apply the SAS congruence theorem, two sides and the angle between them must be congruent. Given \( AE \cong OD \) and \( \angle GAE \cong \angle LOD \), we need one more pair of corresponding sides to be congruent. **Diagrams:** No diagrams or graphs accompany the text. The problem requires identifying the missing piece of information that would complete the SAS criteria for proving triangle congruence. The choices involve various side or angle congruences. Remember, SAS means two sides and the included angle are congruent between two triangles. **Conclusion:** Select the correct option to demonstrate understanding of the SAS criterion for triangle congruency.
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