Identify Parallel and Perpendicular Lines
Read the supplied intersection or direction description.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: Lines A and B intersect at 90°, so they are perpendicular.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Parallel lines lie in one plane and never intersect, even when extended. Perpendicular lines meet at a right angle. Two lines can intersect at a different angle and fit neither category. Segments may look separate, so consider the directions of their full lines, not only the visible endpoints.
Read the supplied intersection or direction description. Classify the relationship using the definitions. For perpendicularity, use the stated ninety-degree angle; for parallelism, use the stated never-meeting equal directions in one plane.
Use stated line relationships rather than only a short sketch. Intersecting lines are perpendicular only when the intersection is a right angle. Sketch arrows at both ends of each line to show extension beyond the visible segment.
- Sketch arrows at both ends of each line to show extension beyond the visible segment.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Read the supplied intersection or direction description.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
Lines A and B intersect at 90°, so they are perpendicular. Lines C and D have matching directions and never meet in the plane, so they are parallel. An intersection at 50° is neither parallel nor perpendicular even if the sketch looks nearly square. Use stated line relationships rather than only a short sketch. Intersecting lines are perpendicular only when the intersection is a right angle. Sketch arrows at both ends of each line to show extension beyond the visible segment.
Check your reasoning
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Helpful tips
- Use stated line relationships rather than only a short sketch.
- Intersecting lines are perpendicular only when the intersection is a right angle.
See the answer and explanation
Perpendicular
A ninety-degree intersection is perpendicular.
Take it further
Classify lines intersecting at 70°. Expected: neither parallel nor perpendicular.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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