Visual Mathematics Challenge: Finding Shared Properties Among Mathematical Figures

Perpendicular Lines with Visual 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
00:00 What is common to all illustrations?
00:02 Perpendicular lines create a right angle at their intersection point
00:05 In this example, the lines form a right angle therefore are perpendicular
00:08 In this one too
00:15 In this one too
00:19 And in this one too
00:22 All lines are perpendicular to each other and that's the answer to the 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 intersect forming a right angle of 90 degrees.

Typically intersecting lines that form a right angle of 90 degrees 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 intersect at exactly 90-degree angles
  • Recognition: Look for square corner symbols or T-shaped intersections
  • Verification: All four angles at intersection must equal 90° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perpendicular with parallel lines
    Don't assume lines that look straight are parallel = wrong classification! Parallel lines never intersect, while perpendicular lines must intersect at right angles. Always look for the intersection point and measure the angle formed.

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 perpendicular just by looking?

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Look for right angle markers (small squares) at intersections, or lines that form perfect T-shapes or L-shapes. The lines should meet at what looks like a corner of a square.

What's the difference between perpendicular and parallel?

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Perpendicular lines intersect at 90° angles, like a plus sign (+). Parallel lines never meet - they're like railroad tracks that go on forever without touching.

Do perpendicular lines have to be straight?

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Yes! Only straight lines can be truly perpendicular. Curved lines or shapes might meet at right angles at specific points, but we typically use 'perpendicular' for straight lines.

Can perpendicular lines be at different angles?

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No - perpendicular lines always meet at exactly 90° 90° . If lines meet at any other angle (like 45° or 120°), they're just intersecting lines, not perpendicular.

How do I measure if lines are actually perpendicular?

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Use a protractor to measure the angle where they meet, or check if a square corner (like from paper) fits perfectly in the angle. The angle must be exactly 90°.

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