Wei Lin drew four line segments on square grid paper: AB (horizontal), CD (horizontal, directly below AB, same length), EF (vertical), and GH (vertical, directly to the right of EF, same length). All four line segments are drawn on the grid so that EF and GH each meet AB and CD at right angles. How many pairs of parallel line segments are there among AB, CD, EF, and GH?
Show Worked Solution
Worked Solution
Step 1: List all C(4,2) = 6 pairs among AB, CD, EF, GH.
Step 2: Determine the direction of each segment.
AB: horizontal
CD: horizontal
EF: vertical
GH: vertical
Step 3: Check each pair.
AB & CD: both horizontal, same direction, never meet → parallel ✓
EF & GH: both vertical, same direction, never meet → parallel ✓
AB & EF: horizontal meets vertical at 90° → perpendicular ✗
AB & GH: horizontal meets vertical at 90° → perpendicular ✗
CD & EF: horizontal meets vertical at 90° → perpendicular ✗
CD & GH: horizontal meets vertical at 90° → perpendicular ✗
Step 4: Parallel pairs = 2 (AB & CD, and EF & GH).
Answer: 2
Correct answer: 2
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