Counting Perpendicular Line Pairs in a Pentagon Diagram

Perpendicular Lines with Right Angle Identification

Determine how many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDDEEE

❤️ 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
00:14 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

Determine how many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDDEEE

2

Step-by-step solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

Our right angles are:

BAE,DEA BAE,DEA

The lines that form angle BAE are: BA+AE

The lines that form angle DEA are: DE+EA

Since in the drawing we have 2 angles of 90 degrees marked, we must have 2 pairs of perpendicular lines.

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines meet at exactly 90 degree angles
  • Technique: Look for small square symbols marking right angles like BAE \angle BAE and DEA \angle DEA
  • Check: Count each right angle symbol once = one pair of perpendicular lines ✓

Common Mistakes

Avoid these frequent errors
  • Counting angles instead of line pairs
    Don't count the 2 right angles as your answer = wrong result! Each right angle represents one pair of perpendicular lines, not individual lines. Always identify which two lines form each right angle.

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 do I know which lines are perpendicular?

+

Look for the small square symbols in the corners where lines meet. These squares indicate 90° angles, which means those two lines are perpendicular to each other.

What's the difference between counting angles and counting line pairs?

+

An angle is the space between two lines, but a line pair refers to the two specific lines that create that angle. Each right angle involves exactly one pair of perpendicular lines.

Can the same line be perpendicular to multiple other lines?

+

Yes! In this pentagon, line AE is perpendicular to both line AB and line ED, creating two different pairs of perpendicular lines.

Why don't we count all the lines in the pentagon?

+

Only lines that meet at exactly 90° are perpendicular. The other angles in this pentagon are not right angles, so those line pairs don't count.

How can I be sure I found all the perpendicular pairs?

+

Systematically check each corner of the figure for square symbols. In this diagram, you should find exactly 2 squares marking the right angles.

🌟 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