Perpendicular Lines Analysis: Identifying 4 Pairs in an Arrow-Shaped Figure

Perpendicular Lines with Right Angle Identification

Determine whether there are 4 pairs of perpendicular lines in the figure below?

AAABBBFFFDDDCCCEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are there 4 pairs of perpendicular lines in the drawing?
00:03 Perpendicular lines create a right angle at the intersection point between the lines
00:08 Let's mark and count all right angles to find the perpendicular lines
00:25 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Determine whether there are 4 pairs of perpendicular lines in the figure below?

AAABBBFFFDDDCCCEEE

2

Step-by-step solution

Remember that perpendicular lines are lines that intersect at a 90-degree angle.

Let's mark the right angles in the drawing:

AAABBBFFFDDDCCCEEEWe can see that we have 4 pairs of perpendicular lines:

AE is perpendicular to AB

BF is perpendicular to AB

AE is perpendicular to EC

BF is perpendicular to FD

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines meet at exactly 90-degree angles
  • Technique: Count right angle symbols at each intersection point
  • Check: Verify each pair forms a perfect square corner ✓

Common Mistakes

Avoid these frequent errors
  • Counting intersections instead of perpendicular pairs
    Don't count how many lines cross = wrong total! Just because lines intersect doesn't mean they're perpendicular. Always check if the intersection forms a 90-degree right angle before counting the pair.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

1234

FAQ

Everything you need to know about this question

How can I tell if two lines are really perpendicular?

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Look for the small square symbol at the intersection point! This symbol specifically marks 90-degree angles. If there's no square symbol, the lines aren't perpendicular even if they cross.

Do I count each perpendicular pair twice?

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No! Each pair of perpendicular lines should be counted only once. For example, if line AB is perpendicular to line CD, that's just one pair, not two.

What if lines look perpendicular but have no right angle symbol?

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In geometry problems, never assume lines are perpendicular just because they look like it! Always rely on the right angle symbols or given information, not just visual appearance.

Can three or more lines all be perpendicular to each other?

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In 2D geometry, only two lines can be perpendicular to each other at any single point. However, multiple pairs of perpendicular lines can exist in the same figure.

How do I systematically count all perpendicular pairs?

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Go through each intersection point one by one. Look for right angle symbols, then identify which two specific lines form that 90-degree angle. List each unique pair only once.

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