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M1-034-A10-V04
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G-CO.1
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M1-034-A10-V04
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 examples to state an equivalent angle-based definition of perpendicular lines, justify the consequence for all \(\text{four}\) formed angles, and explain why crossing alone is insufficient.
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A
term = perpendicular lines; condition = all four angles can have different measures; consequence = right angle unnecessary; nonexample failure = unequal angles are sufficient
B
term = perpendicular lines; condition = lines intersect and at least one formed angle measures 90°; consequence = linear pairs and vertical angles make all four formed angles 90°; nonexample failure = crossing alone does not imply perpendicularity when no angle is 90°
C
term = perpendicular lines; condition = lines cross at any angle; consequence = all crossing lines form right angles; nonexample failure = none
D
term = perpendicular lines; condition = lines are horizontal and vertical; consequence = orientation makes them perpendicular; nonexample failure = slanted lines cannot be perpendicular
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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
