Identifying Perpendicular Lines: Which of Lines 1-4 Form Right Angles?

Perpendicular Lines with Right Angle Verification

Which lines are perpendicular to each other?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Which of the lines are perpendicular?
00:03 Perpendicular lines form a right angle at their intersection point
00:06 In this example, the lines form a right angle
00:11 In this one too
00:15 In this one too
00:21 And in this one too
00:25 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

Which lines are perpendicular to each other?

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2

Step-by-step solution

Let's remember that perpendicular lines form a 90-degree angle with each other.

To check if the lines form a 90-degree angle, we will draw a T at each intersection as follows:

1234We notice that in each of the four drawings, the lines form a 90-degree angle.

Therefore all are correct as all the lines are perpendicular to each other.

3

Final Answer

All answers are correct.

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines intersect to form exactly 90-degree angles
  • Technique: Draw small squares at intersections to check for right angles
  • Verification: All four line pairs show perfect 90° squares at intersections ✓

Common Mistakes

Avoid these frequent errors
  • Assuming lines are perpendicular without checking angles
    Don't just guess perpendicular lines based on how they look = wrong identification! Lines can cross at many different angles, not just 90°. Always verify by drawing right angle markers or measuring the intersection angles.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

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FAQ

Everything you need to know about this question

How can I tell if lines are really perpendicular just by looking?

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You can't be certain just by looking! Lines might appear perpendicular but actually form 85° or 95° angles. Always use the square test - draw small squares at intersections to verify true right angles.

What's the difference between intersecting and perpendicular lines?

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All perpendicular lines intersect, but not all intersecting lines are perpendicular! Intersecting just means they cross somewhere. Perpendicular means they cross at exactly 90° 90° angles.

Do I need to check every intersection point?

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Yes! When two lines are perpendicular, they form four right angles at their intersection. Check that all four angles are exactly 90° by drawing squares in each corner.

Can perpendicular lines be diagonal?

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Absolutely! Perpendicular lines don't have to be horizontal and vertical. As long as they intersect at 90° 90° angles, they're perpendicular - regardless of their orientation.

Why does the answer say 'All answers are correct'?

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This means all four line pairs in the diagram are perpendicular to each other! Each intersection shows perfect right angles, so every line is perpendicular to every other line it crosses.

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