Identifying Perpendicular Line Segments in a Three-Line Geometric Figure

Perpendicular Lines with Right Angle Identification

In the figure there are 3 straight line segments.

Which are perpendicular?

AAABBBEEEFFFCCCDDD

❤️ 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 Found the perpendicular lines
00:04 A perpendicular line is a line that forms a right angle at the intersection point with the second line
00:09 Therefore all these lines are perpendicular
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

In the figure there are 3 straight line segments.

Which are perpendicular?

AAABBBEEEFFFCCCDDD

2

Step-by-step solution

Let's remember that a perpendicular is a line that forms a right angle of 90 degrees with another line.

Let's pay attention to the right angles in the drawing, and note which lines create them:

AB is perpendicular to DC

AB is perpendicular to FE

3

Final Answer

ABDCABFE AB⟂DC \\ AB⟂FE

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines form exact 90-degree right angles
  • Visual Clues: Look for small square symbols marking right angles in diagrams
  • Verification: Count all perpendicular pairs: AB⊥DC and AB⊥FE gives two relationships ✓

Common Mistakes

Avoid these frequent errors
  • Only identifying one perpendicular pair when multiple exist
    Don't stop after finding AB⊥DC = incomplete answer! This misses other perpendicular relationships in the figure. Always examine every line intersection and check for all right angle markers in the diagram.

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 can I tell if lines are perpendicular just by looking?

+

Look for small square symbols at the intersection points! These squares indicate 90-degree angles. Also, perpendicular lines create an L-shape or cross that looks perfectly square.

Can three lines all be perpendicular to each other?

+

Not all at once in 2D! In this figure, line AB is perpendicular to both DC and FE, but DC and FE are not perpendicular to each other - they're actually parallel.

What if I can't see the right angle squares clearly?

+

The squares might be small or faint. Look carefully at each intersection point. You can also use the fact that perpendicular lines create equal adjacent angles of 90 degrees each.

Do I need to write the perpendicular symbol in my answer?

+

Yes! Use the symbol \perp to show perpendicularity clearly. Write it as AB⊥DC rather than just saying "AB and DC are perpendicular."

How many perpendicular pairs should I expect to find?

+

It depends on the figure! In this problem, there are exactly two perpendicular pairs. Don't assume there's always just one - carefully check every intersection.

🌟 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