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M1-034-A10-V03
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G-CO.1
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M1-034-A10-V03
Use precise definitions of angle, circle, perpendicular line, parallel line, and line segment from point/line/distance ideas.
Write a precise definition for perpendicular lines
Problem
Use the displayed example and nonexample to define parallel lines precisely, explain the coplanarity failure for skew lines, and distinguish \(\text{two}\) parallel lines from \(\text{one}\) coincident line.
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A
term = parallel lines; definition = any nonintersecting lines; skew failure = skew lines are parallel; coincident failure = same line is parallel to itself
B
term = parallel lines; definition = coincident lines; skew failure = distinctness unnecessary; coincident failure = same line counts as two
C
term = parallel lines; definition = lines that intersect once far away; skew failure = distance makes intersection irrelevant; coincident failure = same line is parallel
D
term = parallel lines; definition = two distinct coplanar lines that do not intersect; skew failure = nonintersecting lines in different planes are not parallel; coincident failure = the same line is not two distinct parallel lines
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Curriculum context
Standard G-CO.1
Category Geometry
Domain Congruence
Objective Use precise definitions of angle, circle, perpendicular line, parallel line, and line segment from point/line/distance ideas.
Problem type Write a precise definition for perpendicular lines
