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In the image to the right, AGHI = AGJI by SS. Explain why this must be true when only Iwo pairs of segments are marked in the figure. H

In the image to the right, AGHI = AGJI by SS. Explain why this must be true when only Iwo pairs of segments are marked in the figure. H

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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**Text:** In the image to the right, ΔGHI ≅ ΔGJI by SSS. Explain why this must be true when only two pairs of segments are marked in the figure. **Explanation of Diagram:** The image shows two overlapping triangles, ΔGHI and ΔGJI, with point G as a common vertex. The triangles share side GI. The sides GH and HJ are each marked with a single line segment, indicating they are congruent. Likewise, the sides HI and JI are marked with two line segments, indicating they are also congruent. Given this information, the triangles are congruent by the Side-Side-Side (SSS) Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Despite only two pairs of marked segments, the shared side GI completes the requirement for the SSS Postulate.
Transcribed Image Text:**Text:** In the image to the right, ΔGHI ≅ ΔGJI by SSS. Explain why this must be true when only two pairs of segments are marked in the figure. **Explanation of Diagram:** The image shows two overlapping triangles, ΔGHI and ΔGJI, with point G as a common vertex. The triangles share side GI. The sides GH and HJ are each marked with a single line segment, indicating they are congruent. Likewise, the sides HI and JI are marked with two line segments, indicating they are also congruent. Given this information, the triangles are congruent by the Side-Side-Side (SSS) Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Despite only two pairs of marked segments, the shared side GI completes the requirement for the SSS Postulate.
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