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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: Proving Triangle Congruence** **Write a two-column proof to show the triangle congruence.** **Given:** \(\triangle GJK \cong \triangle GJL\) **Diagram:** Below the given information, there is a geometric diagram of two triangles, \(\triangle GJK\) and \(\triangle GJL\), that share a common vertex \(G\) and a common side \(GJ\). **Description of the Diagram:** 1. \(G\) is the vertex where both triangles \(\triangle GJK\) and \(\triangle GJL\) meet. 2. \(K, J,\) and \(L\) are points on the base line, with \(J\) being the midpoint. 3. Line segments \(GK\), \(GJ\), and \(GL\) are drawn. 4. Segment \(JK\) is marked with a single tick mark, indicating it is congruent to segment \(JL\), which is also marked with a single tick mark. 5. Segment \(GJ\) is marked with a double tick mark where it is part of both \(\triangle GJK\) and \(\triangle GJL\). **Proof Structure:** **Statement** | **Reason** --- | --- 1. \(J\) is the midpoint of segment \(KL\) | Given 2. \(JK \cong JL\) | Definition of midpoint 3. \(GJ \cong GJ\) | Reflexive Property 4. \(\angle GJK \cong \angle GJL\) | Vertical Angles are Congruent 5. \(\triangle GJK \cong \triangle GJL\) | SAS Postulate (Side-Angle-Side) To demonstrate triangle congruence using the two-column proof, we rely on the information given in the diagram and apply the relevant geometric properties and postulates accordingly.
Transcribed Image Text:**Title: Proving Triangle Congruence** **Write a two-column proof to show the triangle congruence.** **Given:** \(\triangle GJK \cong \triangle GJL\) **Diagram:** Below the given information, there is a geometric diagram of two triangles, \(\triangle GJK\) and \(\triangle GJL\), that share a common vertex \(G\) and a common side \(GJ\). **Description of the Diagram:** 1. \(G\) is the vertex where both triangles \(\triangle GJK\) and \(\triangle GJL\) meet. 2. \(K, J,\) and \(L\) are points on the base line, with \(J\) being the midpoint. 3. Line segments \(GK\), \(GJ\), and \(GL\) are drawn. 4. Segment \(JK\) is marked with a single tick mark, indicating it is congruent to segment \(JL\), which is also marked with a single tick mark. 5. Segment \(GJ\) is marked with a double tick mark where it is part of both \(\triangle GJK\) and \(\triangle GJL\). **Proof Structure:** **Statement** | **Reason** --- | --- 1. \(J\) is the midpoint of segment \(KL\) | Given 2. \(JK \cong JL\) | Definition of midpoint 3. \(GJ \cong GJ\) | Reflexive Property 4. \(\angle GJK \cong \angle GJL\) | Vertical Angles are Congruent 5. \(\triangle GJK \cong \triangle GJL\) | SAS Postulate (Side-Angle-Side) To demonstrate triangle congruence using the two-column proof, we rely on the information given in the diagram and apply the relevant geometric properties and postulates accordingly.
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