Identifying Perpendicular Lines: Geometric Diagram Analysis

Perpendicular Lines with Right Angle Indicators

Which of the following diagrams shows perpendicular lines?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perpendiculars
00:03 A perpendicular is a line that forms a right angle at the intersection point with the other line
00:07 Therefore all these lines are perpendiculars
00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which of the following diagrams shows perpendicular lines?

2

Step-by-step solution

Remember that a perpendicular line is a line that forms a right angle of 90 degrees with another line.

In answer B, we can identify a right angle, therefore in diagram B there is a perpendicular line.

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines intersect at exactly 90 degrees
  • Visual Clue: Look for small square symbols marking right angles
  • Verification: Check that angle measures exactly 90° with square symbol ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all intersecting lines are perpendicular
    Don't assume intersecting lines are perpendicular without checking angles = wrong identification! Lines can intersect at many different angles (30°, 45°, 60°, etc.). Always look for the specific right angle marker (small square) or 90° measurement.

Practice Quiz

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What do the four figures below have in common?

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FAQ

Everything you need to know about this question

What does the small square symbol mean in geometry diagrams?

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The small square symbol at an intersection point indicates a right angle of exactly 90 degrees. This is the universal symbol that tells you two lines are perpendicular!

Can two lines intersect without being perpendicular?

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Absolutely! Lines can intersect at any angle from 0° to 180°. Only when they meet at exactly 90 degrees are they considered perpendicular.

How can I tell if lines are perpendicular without measuring?

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Look for these visual clues:

  • Small square symbols at intersection points
  • Lines that appear to form perfect corners
  • Explicit 90° angle markings

Do perpendicular lines have to touch each other?

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Yes! Perpendicular lines must intersect (cross each other) to form the 90° angle. If they don't touch, we can't determine if they're perpendicular.

What if I see intersecting lines but no right angle symbol?

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Without the right angle marker, you cannot assume the lines are perpendicular. The lines might intersect at any angle - always look for the square symbol or 90° marking!

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