Geometric Pattern Analysis: Identifying Common Properties in Four Line Configurations

Perpendicular Lines with Visual Angle Markers

What do the four figures 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 the drawings?
00:03 A perpendicular creates a right angle at the intersection point between the lines
00:06 In all examples, the lines form a right angle
00:09 Therefore they are all perpendicular
00:13 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

What do the four figures have in common?

1234

2

Step-by-step solution

Let's remember that perpendicular lines are lines that form a 90-degree angle with each other.

Parallel lines are lines that will never intersect and do not form any angle between them.

In order to examine the types of angles that lines form with each other, we will draw a T at the intersection point of the lines in the following way:

1234

Note that from the drawings we can see that what they all have in common is the right angle, which means that all the lines are perpendicular.

3

Final Answer

All show perpendicular lines.

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines intersect forming exactly 90-degree right angles
  • Recognition: Look for small squares at intersection points indicating perpendicularity
  • Verification: All four angles at intersection must measure 90 degrees ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perpendicular and parallel lines
    Don't assume lines that cross are just intersecting = missing the right angle requirement! Perpendicular specifically means 90-degree angles, not just any crossing. Always look for the square symbol or verify the angle measures exactly 90 degrees.

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 perpendicular without measuring?

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Look for the small square symbol at the intersection point! This universal math symbol indicates a 90-degree angle, showing the lines are perpendicular.

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 form exactly 90-degree angles at their intersection point.

Can lines be both parallel and perpendicular?

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No! Parallel lines never intersect, so they cannot be perpendicular. These are opposite concepts - parallel means never meeting, perpendicular means meeting at right angles.

Why do perpendicular lines form four right angles?

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When two lines intersect, they create four angles that add up to 360 degrees. If one angle is 90 degrees, then all four angles must be 90 degrees due to the properties of vertical and adjacent angles.

Do diagonal lines count as perpendicular?

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Yes! Lines can be perpendicular at any orientation - horizontal/vertical, diagonal, or any angle. What matters is that they intersect at exactly 90 degrees, not their position on the page.

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