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

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Determine which lines are parallel to one another?

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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