Identifying Perpendicular Lines: Visual Analysis of 4 Geometric Figures

Perpendicular Lines with Visual Angle Recognition

Which of the figures show perpendicular lines?

1234

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Step-by-step video solution

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00:00 Which of these lines are perpendicular to each other?
00:02 Perpendicular lines create a right angle at their intersection point
00:05 In this example, the lines form a right angle, therefore they are perpendicular
00:08 In this example, the angle is not right, therefore they are not perpendicular
00:11 In this one too
00:15 In this example, the lines form a right angle, therefore they are perpendicular
00:19 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Which of the figures show perpendicular lines?

1234

2

Step-by-step solution

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

It can be observed that in figures 1 and 3, the angles formed by the lines between them are right angles of 90 degrees.

3

Final Answer

1 and 3

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines form exactly 90-degree right angles
  • Technique: Look for square corner symbols or T-shaped intersections
  • Check: Verify each figure shows lines meeting at perfect right angles ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all intersecting lines are perpendicular
    Don't assume lines are perpendicular just because they cross = wrong identification of figures 2 and 4! Lines can intersect at any angle from 0° to 180°. Always check that the angle is exactly 90 degrees, forming a perfect square corner.

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 really perpendicular without measuring?

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Look for visual clues like square corner symbols (⊥) or lines that form perfect T-shapes or plus signs (+). In this problem, figures 1 and 3 clearly show these right-angle indicators.

What's the difference between intersecting and perpendicular lines?

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

Why aren't figures 2 and 4 perpendicular?

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In figure 2, the lines cross at acute and obtuse angles, not 90°. In figure 4, the lines meet at an angle that's clearly not a right angle - they form a slanted intersection.

Do perpendicular lines have to be the same length?

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No! Perpendicular lines can be any length. What matters is that they meet at exactly 90° 90° . Even a short line can be perpendicular to a long line.

Can I have more than two perpendicular lines?

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Yes! Think of a coordinate grid - it has many perpendicular lines. Any line that meets another at 90° 90° is perpendicular to it, regardless of how many other lines are present.

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