Identifying Perpendicular Lines: Finding 90-Degree Intersections

Perpendicular Lines with Angle Measurement

Which lines are perpendicular to each other?

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Step-by-step video solution

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00:03 Are any of these lines perpendicular?
00:06 Perpendicular lines meet to form a right angle, exactly ninety degrees.
00:12 In this example, the angle is less than ninety degrees, so they are not perpendicular.
00:26 And here, the lines don't meet at all, also not perpendicular.
00:30 And that's how you know which lines are perpendicular!

Step-by-step written solution

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Understand the problem

Which lines are perpendicular to each other?

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Step-by-step solution

Let's remember that perpendicular lines are lines that form an angle of 90 degrees between them.

In each of the answers, we will draw the letter T at the point of intersection of the lines.

Let's examine figure A:

We notice that the lines do form a right angle and the lines are perpendicular to each other.

Let's examine figure B:

We notice that the lines do not meet and do not form any angle; therefore, they are parallel lines and not perpendicular.

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Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines intersect forming exactly 90-degree angles
  • Technique: Draw small squares at intersection points to verify right angles
  • Check: Look for one vertical and one horizontal line meeting ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perpendicular with parallel lines
    Don't assume lines that don't touch are perpendicular = they're actually parallel! Parallel lines never intersect and run in the same direction. Always look for lines that cross each other at exactly 90 degrees.

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 can I tell if lines are exactly 90 degrees apart?

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Look for the square symbol at the intersection point! This small square indicates a right angle. You can also check if one line is perfectly vertical and the other is perfectly horizontal.

What's the difference between perpendicular and intersecting lines?

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All perpendicular lines intersect, but not all intersecting lines are perpendicular! Perpendicular lines must meet at exactly 90 degrees, while other intersecting lines can meet at any angle.

Can diagonal lines be perpendicular too?

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Yes! Lines don't have to be horizontal and vertical to be perpendicular. As long as they meet at a 90-degree angle, any two lines can be perpendicular, even if they're both slanted.

Why do some line pairs in the choices look parallel?

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Parallel lines run in the same direction and never intersect. If lines don't cross each other, they cannot be perpendicular because perpendicular lines must meet at a single point.

How do I remember what perpendicular means?

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Think of the letter "T" or a plus sign "+"! Both show two lines meeting at right angles. You can even draw a small "T" at intersection points to check.

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