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Chaim tried to prove that AJKLE ALMN. K 27 27 J Statement Reason 1 JK = LM = 3 Given JL = LN = 5 Given MZKLJ = mZMNL = 27° Given 4. AJKLE ALMN Side-side- angle congruence What is the first error Chaim made in his proof? Choose 1 answer: Chaim used an invalid reason to justify the congruence of a pair of sides or angles. Chaim only established some of the necessary conditions for a congruence criterion. Chaim established all necessary conditions, but then used an inappropriate congruence criterion. Chaim used a criterion that does not guarantee congruence.

Chaim tried to prove that AJKLE ALMN. K 27 27 J Statement Reason 1 JK = LM = 3 Given JL = LN = 5 Given MZKLJ = mZMNL = 27° Given 4. AJKLE ALMN Side-side- angle congruence What is the first error Chaim made in his proof? Choose 1 answer: Chaim used an invalid reason to justify the congruence of a pair of sides or angles. Chaim only established some of the necessary conditions for a congruence criterion. Chaim established all necessary conditions, but then used an inappropriate congruence criterion. Chaim used a criterion that does not guarantee congruence.

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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### Chaim's Triangle Congruence Proof #### Problem Statement: Chaim attempted to prove that the triangles \( \triangle JKL \cong \triangle LMN \). #### Illustration: The illustration features two triangles: - Triangle \(JKL\) with sides \( JK = 3 \), \( JL = 5 \), and angle \( \angle KLJ = 27^\circ \). - Triangle \(LMN\) with sides \( LM = 3 \), \( LN = 5 \), and angle \( \angle MNL = 27^\circ \). #### Proof Table: | Statement | Reason | |-------------------------------------|----------------------------------------| | 1. \( JK = LM = 3 \) | Given | | 2. \( JL = LN = 5 \) | Given | | 3. \( m\angle KLJ = m\angle MNL = 27^\circ \) | Given | | 4. \( \triangle JKL \cong \triangle LMN \) | Side-Side-Angle congruence | #### Question: What is the first error Chaim made in his proof? ##### Possible Answers: A. Chaim used an invalid reason to justify the congruence of a pair of sides or angles. B. Chaim only established some of the necessary conditions for a congruence criterion. C. Chaim established all necessary conditions but then used an inappropriate congruence criterion. D. Chaim used a criterion that does not guarantee congruence. ##### Explanation: To evaluate the correctness of Chaim's proof, it is essential to understand which congruence conditions (criteria) are valid in proving triangle congruence. In this case: - **Side-Side-Angle (SSA)** is not a valid criterion for triangle congruence. - **Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS),** and **Side-Side-Side (SSS)** are the recognized criteria for triangle congruence. Given this, Chaim's error lies in the inappropriate use of the SSA criterion in statement 4. The correct answer is: **D. Chaim used a criterion that does not guarantee congruence.**
Transcribed Image Text:### Chaim's Triangle Congruence Proof #### Problem Statement: Chaim attempted to prove that the triangles \( \triangle JKL \cong \triangle LMN \). #### Illustration: The illustration features two triangles: - Triangle \(JKL\) with sides \( JK = 3 \), \( JL = 5 \), and angle \( \angle KLJ = 27^\circ \). - Triangle \(LMN\) with sides \( LM = 3 \), \( LN = 5 \), and angle \( \angle MNL = 27^\circ \). #### Proof Table: | Statement | Reason | |-------------------------------------|----------------------------------------| | 1. \( JK = LM = 3 \) | Given | | 2. \( JL = LN = 5 \) | Given | | 3. \( m\angle KLJ = m\angle MNL = 27^\circ \) | Given | | 4. \( \triangle JKL \cong \triangle LMN \) | Side-Side-Angle congruence | #### Question: What is the first error Chaim made in his proof? ##### Possible Answers: A. Chaim used an invalid reason to justify the congruence of a pair of sides or angles. B. Chaim only established some of the necessary conditions for a congruence criterion. C. Chaim established all necessary conditions but then used an inappropriate congruence criterion. D. Chaim used a criterion that does not guarantee congruence. ##### Explanation: To evaluate the correctness of Chaim's proof, it is essential to understand which congruence conditions (criteria) are valid in proving triangle congruence. In this case: - **Side-Side-Angle (SSA)** is not a valid criterion for triangle congruence. - **Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS),** and **Side-Side-Side (SSS)** are the recognized criteria for triangle congruence. Given this, Chaim's error lies in the inappropriate use of the SSA criterion in statement 4. The correct answer is: **D. Chaim used a criterion that does not guarantee congruence.**
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