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Which angle e 7, 3, 4 5/6 7/8 9. g O A. Z1 O B. 2 C. Z3 D. Z4

Which angle e 7, 3, 4 5/6 7/8 9. g O A. Z1 O B. 2 C. Z3 D. Z4

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.5: The Distance And Midpoint Formulas
Problem 2C
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### Which angle is congruent to ∠8? Select all that apply. The diagram provided features two parallel lines, \( e \) and \( f \), intersected by a transversal \( g \). The points of intersection form eight angles, labeled as follows: - On the upper line \( e \): - ∠1 and ∠2 above the line \( e \) - ∠3 and ∠4 below the line \( e \) - On the lower line \( f \): - ∠5 and ∠6 above the line \( f \) - ∠7 and ∠8 below the line \( f \) The question requires identifying all the angles congruent to ∠8. ### Answer Choices - A. ∠1 - B. ∠2 - C. ∠3 - D. ∠4 To determine congruent angles, consider the following relationships between angles formed by parallel lines and a transversal: - Corresponding Angles - Alternate Interior Angles - Alternate Exterior Angles - Consecutive Interior Angles ### Explanation ∠8 is located below line \( f \) and to the right of the transversal \( g \). - **Alternate Interior Angles**: These are angles on opposite sides of the transversal and inside the two parallel lines. ∠8 and ∠5 are alternate interior angles. - **Corresponding Angles**: These are angles in matching corners when two lines are crossed by another line (the transversal). ∠8 and ∠4 are corresponding angles. - **Alternate Exterior Angles**: Not applicable here for ∠8. - **Consecutive Interior Angles**: Not applicable here for ∠8. Therefore, angles congruent to ∠8 are: - ∠4 (according to the corresponding angles postulate) ### Conclusion Select the following: - D. ∠4
Transcribed Image Text:### Which angle is congruent to ∠8? Select all that apply. The diagram provided features two parallel lines, \( e \) and \( f \), intersected by a transversal \( g \). The points of intersection form eight angles, labeled as follows: - On the upper line \( e \): - ∠1 and ∠2 above the line \( e \) - ∠3 and ∠4 below the line \( e \) - On the lower line \( f \): - ∠5 and ∠6 above the line \( f \) - ∠7 and ∠8 below the line \( f \) The question requires identifying all the angles congruent to ∠8. ### Answer Choices - A. ∠1 - B. ∠2 - C. ∠3 - D. ∠4 To determine congruent angles, consider the following relationships between angles formed by parallel lines and a transversal: - Corresponding Angles - Alternate Interior Angles - Alternate Exterior Angles - Consecutive Interior Angles ### Explanation ∠8 is located below line \( f \) and to the right of the transversal \( g \). - **Alternate Interior Angles**: These are angles on opposite sides of the transversal and inside the two parallel lines. ∠8 and ∠5 are alternate interior angles. - **Corresponding Angles**: These are angles in matching corners when two lines are crossed by another line (the transversal). ∠8 and ∠4 are corresponding angles. - **Alternate Exterior Angles**: Not applicable here for ∠8. - **Consecutive Interior Angles**: Not applicable here for ∠8. Therefore, angles congruent to ∠8 are: - ∠4 (according to the corresponding angles postulate) ### Conclusion Select the following: - D. ∠4
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