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The diagram below shows two parallel lines, m and n, cut by a transversal, k. Angles A, B, and C are shown in the diagram. B. A student writes a proof to show that the corresponding angles, A and B, are congruent. The student's proof is shown below. Statements 1. m ||n Reasons Given Vertical angles are congruent 2. ZA= ZC Vertical angles are congruent 3. ZB LC 4. ZA ZB Transitive Property Which option describes the validity of Reasons 2 and 3? A Both Reason 2 and Reason 3 are correct as shown in the table. Reason 2 is correct, but Reason 3 should be "Alternate interior angles are congruent". C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct. D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent". O O B.

The diagram below shows two parallel lines, m and n, cut by a transversal, k. Angles A, B, and C are shown in the diagram. B. A student writes a proof to show that the corresponding angles, A and B, are congruent. The student's proof is shown below. Statements 1. m ||n Reasons Given Vertical angles are congruent 2. ZA= ZC Vertical angles are congruent 3. ZB LC 4. ZA ZB Transitive Property Which option describes the validity of Reasons 2 and 3? A Both Reason 2 and Reason 3 are correct as shown in the table. Reason 2 is correct, but Reason 3 should be "Alternate interior angles are congruent". C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct. D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent". O O B.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The diagram shows two parallel lines, \( m \) and \( n \), intersected by a transversal, \( k \). Angles \( A \), \( B \), and \( C \) are marked in the diagram. A student has written a proof to demonstrate that the corresponding angles, \( A \) and \( B \), are congruent. The proof is outlined in the following table: | Statements | Reasons | |----------------------------------|---------------------------------| | 1. \( m \parallel n \) | Given | | 2. \( \angle A \cong \angle C \) | Vertical angles are congruent | | 3. \( \angle B \cong \angle C \) | Vertical angles are congruent | | 4. \( \angle A \cong \angle B \) | Transitive Property | The task asks to evaluate the validity of Reasons 2 and 3: A. Both Reason 2 and Reason 3 are correct as shown in the table. B. Reason 2 is correct, but Reason 3 should be "Alternate interior angles are congruent". C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct. D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent".
Transcribed Image Text:The diagram shows two parallel lines, \( m \) and \( n \), intersected by a transversal, \( k \). Angles \( A \), \( B \), and \( C \) are marked in the diagram. A student has written a proof to demonstrate that the corresponding angles, \( A \) and \( B \), are congruent. The proof is outlined in the following table: | Statements | Reasons | |----------------------------------|---------------------------------| | 1. \( m \parallel n \) | Given | | 2. \( \angle A \cong \angle C \) | Vertical angles are congruent | | 3. \( \angle B \cong \angle C \) | Vertical angles are congruent | | 4. \( \angle A \cong \angle B \) | Transitive Property | The task asks to evaluate the validity of Reasons 2 and 3: A. Both Reason 2 and Reason 3 are correct as shown in the table. B. Reason 2 is correct, but Reason 3 should be "Alternate interior angles are congruent". C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct. D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent".
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