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7. Which pairs of angles are not congruent? E A 1/2 C O 47 and 48 O 24 and 28 22 and 26 21 and 25 F 3/4 5/6 7/8 B D

7. Which pairs of angles are not congruent? E A 1/2 C O 47 and 48 O 24 and 28 22 and 26 21 and 25 F 3/4 5/6 7/8 B D

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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**Question 7: Which pairs of angles are not congruent?** Below is a diagram comprising three intersecting lines, labeled as follows: - Line \( AB \) extends horizontally from point \( A \) on the left to point \( B \) on the right. - Line \( CD \) extends horizontally from point \( C \) on the left to point \( D \) on the right, below line \( AB \). - Line \( EF \) intersects lines \( AB \) and \( CD \) diagonally, from the top right to the bottom left, and continues beyond both points of intersection. The intersections create several angles, labeled \(1\) through \(8\) as follows: - Line \( EF \) intersects line \( AB \), creating angles \(1\), \(2\), \(3\), and \(4\). - Line \( EF \) intersects line \( CD \), creating angles \(5\), \(6\), \(7\), and \(8\). ### Angles and Their Locations - **Angles 1 and 2:** Above line \( AB \), between \( AB \) and \( EF \). - **Angles 3 and 4:** Below line \( AB \), between \( AB \) and \( EF \). - **Angles 5 and 6:** Above line \( CD \), between \( CD \) and \( EF \). - **Angles 7 and 8:** Below line \( CD \), between \( CD \) and \( EF \). ### Question Options The problem asks which pairs of angles are not congruent. The available options are: 1. \(\angle 7\) and \(\angle 8\) 2. \(\angle 4\) and \(\angle 8\) 3. \(\angle 2\) and \(\angle 6\) 4. \(\angle 1\) and \(\angle 5\) ### Identifying Congruent Angles Adjacent angles and vertically opposite angles created by intersecting lines can provide congruent pairs. Based on the properties of parallel lines cut by a transversal, corresponding angles (e.g., \(\angle 1\) and \(\angle 5\)), alternate interior angles (e.g., \(\angle 3\) and \(\angle 6\)), and vertically opposite angles (e.g., \(\angle 1\) and
Transcribed Image Text:**Question 7: Which pairs of angles are not congruent?** Below is a diagram comprising three intersecting lines, labeled as follows: - Line \( AB \) extends horizontally from point \( A \) on the left to point \( B \) on the right. - Line \( CD \) extends horizontally from point \( C \) on the left to point \( D \) on the right, below line \( AB \). - Line \( EF \) intersects lines \( AB \) and \( CD \) diagonally, from the top right to the bottom left, and continues beyond both points of intersection. The intersections create several angles, labeled \(1\) through \(8\) as follows: - Line \( EF \) intersects line \( AB \), creating angles \(1\), \(2\), \(3\), and \(4\). - Line \( EF \) intersects line \( CD \), creating angles \(5\), \(6\), \(7\), and \(8\). ### Angles and Their Locations - **Angles 1 and 2:** Above line \( AB \), between \( AB \) and \( EF \). - **Angles 3 and 4:** Below line \( AB \), between \( AB \) and \( EF \). - **Angles 5 and 6:** Above line \( CD \), between \( CD \) and \( EF \). - **Angles 7 and 8:** Below line \( CD \), between \( CD \) and \( EF \). ### Question Options The problem asks which pairs of angles are not congruent. The available options are: 1. \(\angle 7\) and \(\angle 8\) 2. \(\angle 4\) and \(\angle 8\) 3. \(\angle 2\) and \(\angle 6\) 4. \(\angle 1\) and \(\angle 5\) ### Identifying Congruent Angles Adjacent angles and vertically opposite angles created by intersecting lines can provide congruent pairs. Based on the properties of parallel lines cut by a transversal, corresponding angles (e.g., \(\angle 1\) and \(\angle 5\)), alternate interior angles (e.g., \(\angle 3\) and \(\angle 6\)), and vertically opposite angles (e.g., \(\angle 1\) and
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