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.

3

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

The lines below are not the same size, but are they parallel?

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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