Counting Perpendicular Lines: Geometric Diagram Analysis Exercise

Perpendicular Lines with Right Angle Identification

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

AAABBBCCC

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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
00:12 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?

AAABBBCCC

2

Step-by-step solution

Remember that perpendicular lines are vertical lines that form a right angle of 90 degrees between them.

The right angle we have in the drawing is angle ABC.

The lines that form the angle ABC are AB and BC.

Since we have one marked angle in the triangle, we must have a pair of perpendicular lines.

3

Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines meet at exactly 90 degrees
  • Recognition: Look for right angle markers like squares in corners
  • Counting: Count each pair once: AB ⊥ BC = 1 pair ✓

Common Mistakes

Avoid these frequent errors
  • Counting lines instead of pairs of lines
    Don't count AB, BC as 2 separate items = wrong count of 2! You need pairs of lines that meet perpendicularly. Always count how many different pairs of perpendicular lines exist, not individual line segments.

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 if two lines are perpendicular?

+

Look for right angle markers (small squares) at the intersection point, or check if the angle measures exactly 90° 90° . In this diagram, the small square at point B shows that lines AB and BC are perpendicular.

What's the difference between counting lines and counting pairs?

+

A pair means two lines that intersect perpendicularly. Even if you see 3 lines, you might only have 1 perpendicular pair. Always ask: which two lines form a right angle together?

Can three lines all be perpendicular to each other?

+

In a flat (2D) diagram, no. You can have at most one pair of perpendicular lines meeting at any point. Three mutually perpendicular lines only exist in 3D space.

What if I don't see a right angle marker?

+

Look carefully at the intersection angles. If an angle appears to be exactly 90° 90° (like a perfect corner), the lines are likely perpendicular. However, marked right angles are the most reliable indicator.

Why is the answer 1 and not 2 or 3?

+

Count the pairs of perpendicular lines: AB and BC form one right angle at point B. Even though there are 3 line segments total (AB, BC, AC), only one pair is perpendicular to each other.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallel and Perpendicular Lines questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations