Line Pattern Recognition: Comparing Four Geometric Configurations

Perpendicular Lines with Right Angle Recognition

What do the four figures below have in common?

1234

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 What do all these drawings have in common?
00:06 Perpendicular lines meet to form a right angle at their intersection.
00:11 In this example, the lines create a right angle, so they are perpendicular.
00:17 And in this one, they are also perpendicular.
00:20 These lines are perpendicular too.
00:23 Again, we see perpendicular lines here.
00:27 All lines are perpendicular to each other. That's the answer to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What do the four figures below have in common?

1234

2

Step-by-step solution

Upon observation we can see that all the lines form a right angle of 90 degrees with each other.

Typically lines that form a right angle of 90 degrees with each other are perpendicular and vertical lines.

Therefore, the correct answer is a.

3

Final Answer

All the figures are perpendicular

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines always intersect forming 90-degree right angles
  • Recognition: Look for square corner symbol or lines meeting at right angles
  • Verification: All four figures show lines meeting at exactly 90 degrees ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perpendicular with parallel lines
    Don't assume lines that look similar are parallel = wrong classification! Parallel lines never intersect while these lines clearly meet at right angles. Always check if lines intersect at 90 degrees to identify perpendicular relationships.

Practice Quiz

Test your knowledge with interactive questions

The lines below are not the same size, but are they parallel?

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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Look for the square corner symbol or lines that meet at what appears to be a 90-degree angle. In these figures, you can see the lines intersect to form right angles, not acute or obtuse angles.

What's the difference between perpendicular and parallel lines?

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Perpendicular lines intersect at 90 degrees, while parallel lines never intersect at all - they stay the same distance apart forever. These figures show intersecting lines, so they can't be parallel!

Do all the figures have to look exactly the same to have something in common?

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No! They can have different orientations but still share the same mathematical property. Here, all four figures show perpendicular lines even though they're positioned differently.

Why isn't the answer about acute or obtuse angles?

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An acute angle is less than 90 degrees, and an obtuse angle is greater than 90 degrees. All these figures show exactly 90-degree angles, which are called right angles - the defining feature of perpendicular lines.

Can perpendicular lines be in any position?

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Yes! Perpendicular lines can be horizontal and vertical like a plus sign, or diagonal like an X. What matters is that they meet at exactly 90 degrees, regardless of their orientation.

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