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Considering the figure to the right, correct the proof of the Perpendicular Transversal Theorem. Given: <1 = 24 and ₂ 1 t at 22. Prove: 1₂ Lt Statements 24; 4₂1 t at 22 1.21 2. - || 1 3. 22 is a right angle 4. m/2 = 90° 5. m/2 + m24 = 180° Two of the reasons in the chart below do not correspond to the correct statements. Circle those two reasons. 6. 90° + m24 = 180° 7. m/4= 90° 4₂ 8. 1₂ It 12 t 1. Given 12 34 Reasons 2. Consecutive Angles Theorem 3. Definition of perpendicular lines 4. Definition of right angle 5. Converse of Alternate Interior Angles Theorem 6. Substitution property 7. Subtraction property of equality 8. Definition of perpendicular lines

Considering the figure to the right, correct the proof of the Perpendicular Transversal Theorem. Given: <1 = 24 and ₂ 1 t at 22. Prove: 1₂ Lt Statements 24; 4₂1 t at 22 1.21 2. - || 1 3. 22 is a right angle 4. m/2 = 90° 5. m/2 + m24 = 180° Two of the reasons in the chart below do not correspond to the correct statements. Circle those two reasons. 6. 90° + m24 = 180° 7. m/4= 90° 4₂ 8. 1₂ It 12 t 1. Given 12 34 Reasons 2. Consecutive Angles Theorem 3. Definition of perpendicular lines 4. Definition of right angle 5. Converse of Alternate Interior Angles Theorem 6. Substitution property 7. Subtraction property of equality 8. Definition of perpendicular lines

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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Considering the figure to the right, correct the proof of the Perpendicular Transversal Theorem.

**Title: Correcting the Proof of the Perpendicular Transversal Theorem** **Problem Statement:** Consider the figure provided. Correct the proof of the Perpendicular Transversal Theorem. **Given:** - \(\angle 1 \cong \angle 4\) and \(l_1 \perp t\) at \(\angle 2\). **Prove:** - \(l_2 \perp t\). **Instructions:** Identify and circle two reasons in the chart below that do not correspond to the correct statements. --- **Diagram Explanation:** The diagram shows two parallel lines \(l_1\) and \(l_2\) cut by a transversal \(t\). The diagram is labeled with angles \(1\), \(2\), \(3\), and \(4\) at the intersections. \(l_1\) is perpendicular to \(t\) at \(\angle 2\). --- **Statements and Reasons:** | Statements | Reasons | |-------------------------------------------------|--------------------------------------------| | 1. \(\angle 1 \cong \angle 4; l_1 \perp t\) at \(\angle 2\) | 1. Given | | 2. \(l_1 \parallel l_2\) | 2. Consecutive Angles Theorem | | 3. \(\angle 2\) is a right angle | 3. Definition of perpendicular lines | | 4. \(m\angle 2 = 90^\circ\) | 4. Definition of right angle | | 5. \(m\angle 2 + m\angle 4 = 180^\circ\) | 5. Converse of Alternate Interior Angles Theorem | | 6. \(90^\circ + m\angle 4 = 180^\circ\) | 6. Substitution property | | 7. \(m\angle 4 = 90^\circ\) | 7. Subtraction property of equality | | 8. \(l_2 \perp t\) | 8. Definition of perpendicular lines | **Note:** Two reasons (2 and 5) do not correspond correctly to their respective statements. Use logical reasoning to identify incorrect justifications and correct them to support the proof adequately.
Transcribed Image Text:**Title: Correcting the Proof of the Perpendicular Transversal Theorem** **Problem Statement:** Consider the figure provided. Correct the proof of the Perpendicular Transversal Theorem. **Given:** - \(\angle 1 \cong \angle 4\) and \(l_1 \perp t\) at \(\angle 2\). **Prove:** - \(l_2 \perp t\). **Instructions:** Identify and circle two reasons in the chart below that do not correspond to the correct statements. --- **Diagram Explanation:** The diagram shows two parallel lines \(l_1\) and \(l_2\) cut by a transversal \(t\). The diagram is labeled with angles \(1\), \(2\), \(3\), and \(4\) at the intersections. \(l_1\) is perpendicular to \(t\) at \(\angle 2\). --- **Statements and Reasons:** | Statements | Reasons | |-------------------------------------------------|--------------------------------------------| | 1. \(\angle 1 \cong \angle 4; l_1 \perp t\) at \(\angle 2\) | 1. Given | | 2. \(l_1 \parallel l_2\) | 2. Consecutive Angles Theorem | | 3. \(\angle 2\) is a right angle | 3. Definition of perpendicular lines | | 4. \(m\angle 2 = 90^\circ\) | 4. Definition of right angle | | 5. \(m\angle 2 + m\angle 4 = 180^\circ\) | 5. Converse of Alternate Interior Angles Theorem | | 6. \(90^\circ + m\angle 4 = 180^\circ\) | 6. Substitution property | | 7. \(m\angle 4 = 90^\circ\) | 7. Subtraction property of equality | | 8. \(l_2 \perp t\) | 8. Definition of perpendicular lines | **Note:** Two reasons (2 and 5) do not correspond correctly to their respective statements. Use logical reasoning to identify incorrect justifications and correct them to support the proof adequately.
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