Counting Perpendicular Line Pairs: Geometric Shape Analysis

Perpendicular Lines with Right Angle Identification

How many pairs of perpendicular lines are there in the diagram?

AAABBBCCCDDDEEEFFF

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 How many perpendiculars are there in the drawing?
00:03 A perpendicular creates a right angle at the intersection point between the lines
00:07 Let's mark and count all the right angles
00:14 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

How many pairs of perpendicular lines are there in the diagram?

AAABBBCCCDDDEEEFFF

2

Step-by-step solution

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

The right angles we have in the drawing are:

FAB,CDE FAB,CDE

The lines that create the angle FAB are: FA + AB

The lines that create the angle CDE are: CD + DE

Since we have 2 angles marked in the diagram, we therefore also have 2 pairs of perpendicular lines.

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines form exactly 90-degree right angles at intersection
  • Technique: Count right angle markers - each square symbol represents one pair
  • Check: Verify each pair shares a common vertex where lines meet at 90° ✓

Common Mistakes

Avoid these frequent errors
  • Counting individual lines instead of pairs
    Don't count 6 lines and think there are 6 pairs = wrong approach! This confuses individual line segments with perpendicular relationships. Always count the right angle markers - each square symbol represents exactly one pair of perpendicular lines.

Practice Quiz

Test your knowledge with interactive questions

Determine which lines are parallel to one another?

FAQ

Everything you need to know about this question

How do I know which lines are perpendicular just by looking?

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Look for the small square symbols in the corners! These markers specifically show where two lines meet at exactly 90 degrees. In this diagram, you can see squares at angles FAB FAB and CDE CDE .

Why isn't every corner in the shape a right angle?

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Great observation! Only corners with the square marker symbol are confirmed to be 90-degree angles. Other corners might look square but aren't marked as right angles, so we can't assume they're perpendicular.

What's the difference between lines and line segments in this problem?

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For counting perpendicular pairs, it doesn't matter! Whether we call them lines or line segments, we're looking for two straight paths that meet at exactly 90 degrees, marked by the square symbols.

Could there be more than 2 pairs that I'm missing?

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No! Count the right angle markers carefully - there are exactly 2 square symbols in this diagram. Each square represents one pair of perpendicular lines, so the answer is definitely 2.

How do I name the perpendicular line pairs correctly?

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Use the three points that form each right angle. For angle FAB FAB , the perpendicular lines are FA and AB. For angle CDE CDE , they are CD and DE.

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