In the figure, line EF is a horizontal line. Line GH crosses EF at point X and forms a 90° angle with EF. Line KL is drawn so that it is always the same distance from EF and will never cross EF no matter how far it is extended. How many pairs of perpendicular lines are there among EF, GH, and KL?
Show Worked Solution
Worked Solution
Step 1: List all pairs of lines among EF, GH, and KL:
Pair 1: EF and GH
Pair 2: EF and KL
Pair 3: GH and KL
Step 2: Check each pair.
EF and GH: GH meets EF at 90° (given) → perpendicular ✓
EF and KL: KL is always the same distance from EF and never crosses it → parallel, NOT perpendicular ✗
GH and KL: KL ∥ EF and GH ⊥ EF, so GH must also meet KL at 90° → perpendicular ✓
Step 3: Count perpendicular pairs: 2.
Answer: 2
Correct answer: 2
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