Geometry Problem: Which Lines Form Perfect Right Angles?

Perpendicular Lines with Visual Identification

Which lines are perpendicular to each other?

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Step-by-step video solution

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00:00 Which lines are perpendicular?
00:02 Perpendicular lines form a right angle at their intersection point
00:05 In this example, the angle between the lines is unknown
00:08 In this example, the lines form a right angle, therefore they are perpendicular
00:15 In this example, the lines never intersect and therefore are parallel
00:26 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Which lines are perpendicular to each other?

2

Step-by-step solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where it can be seen that the lines form a right angle of 90 degrees between them is drawing A.

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Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines form exactly 90-degree right angles
  • Visual Check: Look for small square symbols marking right angles
  • Verification: Only intersecting lines with square corner markers are perpendicular ✓

Common Mistakes

Avoid these frequent errors
  • Thinking all intersecting lines are perpendicular
    Don't assume any two crossing lines are perpendicular = wrong identification! Lines can intersect at many different angles (30°, 45°, 60°, etc.). Always look for the small square symbol or verify the angle measures exactly 90°.

Practice Quiz

Test your knowledge with interactive questions

Which of the diagrams contain parallel lines?

AB

FAQ

Everything you need to know about this question

How can I tell if lines are perpendicular just by looking?

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Look for the small square symbol at the intersection point! This square indicates a 90° angle. Without this marker, you cannot assume lines are perpendicular even if they look like they might be.

What's the difference between intersecting and perpendicular lines?

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All perpendicular lines intersect, but not all intersecting lines are perpendicular! Intersecting lines can meet at any angle, while perpendicular lines must meet at exactly 90°.

Why do parallel lines never count as perpendicular?

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Parallel lines never touch or intersect, so they can't form any angle at all! Since perpendicular lines must intersect at 90°, parallel lines can never be perpendicular.

Can diagonal lines be perpendicular?

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Absolutely! Lines don't have to be horizontal and vertical to be perpendicular. Any two lines that meet at exactly 90° are perpendicular, regardless of their orientation.

What if the lines look almost perpendicular but no square is shown?

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Without the square symbol, you cannot assume they're perpendicular! In math problems, visual markers are crucial - if there's no right angle symbol, the lines aren't considered perpendicular.

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