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These triangles are congruent by the triangle congruence postulate [ ? ]. A. Neither, they are not congruent В. ASA С. AS

These triangles are congruent by the triangle congruence postulate [ ? ]. A. Neither, they are not congruent В. ASA С. AS

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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### Triangle Congruence Postulates #### Understanding Congruence with Triangles In this section, we explore how to determine triangle congruence. Given two triangles, they can be considered congruent if they have exactly the same three sides and exactly the same three angles. We use specific postulates to verify this congruence. #### Visual Aid: Triangle Congruence Explanation The image depicts two overlapping triangles, with corresponding angles marked to demonstrate a congruence check: ![Triangles Diagram](image_placeholder) - **Angle 1**: Marked on the upper tip of the more left-positioned triangle. - **Angle 2**: Marked on the lower tip near the bottom of the same triangle. These markings help in identifying and comparing the corresponding parts of the triangles. #### Question: Identifying the Postulate **Prompt:** "These triangles are congruent by the triangle congruence postulate [ ? ]." **Options:** A. Neither, they are not congruent B. ASA (Angle-Side-Angle) C. AAS (Angle-Angle-Side) **Explanation:** To determine the correct postulate: 1. **ASA (Angle-Side-Angle) Postulate**: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. 2. **AAS (Angle-Angle-Side) Postulate**: If two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, the triangles are congruent. Carefully review the diagram and the relationship of the angles and sides to determine the correct postulate that proves congruence for the given triangles.
Transcribed Image Text:### Triangle Congruence Postulates #### Understanding Congruence with Triangles In this section, we explore how to determine triangle congruence. Given two triangles, they can be considered congruent if they have exactly the same three sides and exactly the same three angles. We use specific postulates to verify this congruence. #### Visual Aid: Triangle Congruence Explanation The image depicts two overlapping triangles, with corresponding angles marked to demonstrate a congruence check: ![Triangles Diagram](image_placeholder) - **Angle 1**: Marked on the upper tip of the more left-positioned triangle. - **Angle 2**: Marked on the lower tip near the bottom of the same triangle. These markings help in identifying and comparing the corresponding parts of the triangles. #### Question: Identifying the Postulate **Prompt:** "These triangles are congruent by the triangle congruence postulate [ ? ]." **Options:** A. Neither, they are not congruent B. ASA (Angle-Side-Angle) C. AAS (Angle-Angle-Side) **Explanation:** To determine the correct postulate: 1. **ASA (Angle-Side-Angle) Postulate**: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. 2. **AAS (Angle-Angle-Side) Postulate**: If two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, the triangles are congruent. Carefully review the diagram and the relationship of the angles and sides to determine the correct postulate that proves congruence for the given triangles.
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