Identify Perpendicular Lines: Finding 90° Intersections Among Lines 1-4

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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00:00 Which lines are perpendicular?
00:03 Perpendicular lines create a right angle at their intersection point
00:06 In this example, the lines create a right angle
00:09 In this one too
00:16 And in this one
00:24 In this example, the lines create an angle greater than 90
00:32 And this is the solution to the question

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 vertical lines that create a 90-degree angle with each other.

To examine the types of angles that lines create with each other, let's draw a T at the intersection point of the lines in the following way:

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Note that in drawings 1+4 we see right angles, meaning the lines are perpendicular to each other.

In the other drawings, the angles created are greater or smaller than 90 degrees, therefore the lines are not perpendicular.

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Final Answer

1 and 4

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 identify right angles
  • Check: Look for perfect square corners where lines meet ✓

Common Mistakes

Avoid these frequent errors
  • Confusing steep lines with perpendicular lines
    Don't assume lines are perpendicular just because they look steep or slanted = wrong identification! A line can be very steep but still not form 90° angles with other lines. Always check if the intersection creates perfect right angles (square corners).

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 two lines are really perpendicular?

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Look for perfect square corners where the lines meet! Perpendicular lines create four 90° 90° angles at their intersection point. If you can imagine placing a small square perfectly in the corner, they're perpendicular.

Do perpendicular lines have to be horizontal and vertical?

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No! Perpendicular lines can be at any angle as long as they meet at exactly 90° 90° . They could both be diagonal - what matters is the right angle where they intersect.

Why do some line pairs in this problem look close to perpendicular but aren't?

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Lines 2 and 3 form angles that are close to 90° 90° but not exactly. In math, 'close' isn't good enough - perpendicular means exactly 90° 90° , no more, no less!

How do I identify perpendicular lines in a diagram with many lines?

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Check each pair systematically! Look for intersections that form perfect square corners. In this problem, only lines 1 and 4 meet this test - all other pairs create angles greater or less than 90° 90° .

Can two lines be perpendicular if they don't touch?

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No! For lines to be perpendicular, they must intersect (cross each other) and form 90° 90° angles at that intersection point. Parallel lines never touch, so they can't be perpendicular.

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