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If AB is parallel to CD, which statement must be true? CD. O A. The perpendicular distance between and D АВ increases as the lines are traversed left to right. O B. The perpendicular distance between B and decreases as the lines are traversed right to left. OC. R and CD do not intersect. АВ O D. R and intersect at 90° angles. АВ Next

If AB is parallel to CD, which statement must be true? CD. O A. The perpendicular distance between and D АВ increases as the lines are traversed left to right. O B. The perpendicular distance between B and decreases as the lines are traversed right to left. OC. R and CD do not intersect. АВ O D. R and intersect at 90° angles. АВ Next

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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**Parallel Lines and Their Properties** **Question:** If \(\overleftrightarrow{AB}\) is parallel to \(\overleftrightarrow{CD}\), which statement must be true? **Options:** - **A.** The perpendicular distance between \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) increases as the lines are traversed left to right. - **B.** The perpendicular distance between \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) decreases as the lines are traversed right to left. - **C.** \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) do not intersect. - **D.** \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) intersect at 90° angles. **Explanation:** In geometry, when two lines are parallel, they never intersect or meet, no matter how far they are extended. This means that the perpendicular distance between these two lines remains constant. - **Option A** suggests that the distance increases, which would imply that the lines are diverging, not parallel. - **Option B** suggests that the distance decreases, implying that the lines are converging, not parallel. - **Option C** accurately states that parallel lines do not intersect. - **Option D** suggests that the lines intersect at a 90° angle, which contradicts the definition of parallel lines. **Therefore, the correct answer is C: \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) do not intersect.** This scenario aligns with the fundamental property of parallel lines in Euclidean geometry.
Transcribed Image Text:**Parallel Lines and Their Properties** **Question:** If \(\overleftrightarrow{AB}\) is parallel to \(\overleftrightarrow{CD}\), which statement must be true? **Options:** - **A.** The perpendicular distance between \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) increases as the lines are traversed left to right. - **B.** The perpendicular distance between \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) decreases as the lines are traversed right to left. - **C.** \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) do not intersect. - **D.** \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) intersect at 90° angles. **Explanation:** In geometry, when two lines are parallel, they never intersect or meet, no matter how far they are extended. This means that the perpendicular distance between these two lines remains constant. - **Option A** suggests that the distance increases, which would imply that the lines are diverging, not parallel. - **Option B** suggests that the distance decreases, implying that the lines are converging, not parallel. - **Option C** accurately states that parallel lines do not intersect. - **Option D** suggests that the lines intersect at a 90° angle, which contradicts the definition of parallel lines. **Therefore, the correct answer is C: \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) do not intersect.** This scenario aligns with the fundamental property of parallel lines in Euclidean geometry.
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