Geometric Pattern Analysis: Finding Common Properties in 4 Line Configurations

Line Relationships with Intersection Properties

What do the 4 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 the drawings?
00:02 The lines intersect the line into 2 equal parts
00:05 In this example the segments are equal therefore the lines intersect
00:08 Also in this one
00:11 Also in this one
00:16 And also in this one
00:20 All lines intersect each other and that is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What do the 4 figures below have in common?

1234

2

Step-by-step solution

Let's first think about the different definitions of various lines.

We can see that what is common to all of the lines is that they intersect each other, meaning they have a point of intersection.

Remember that lines that cross each other are lines that will meet at a certain point.

Therefore, the correct answer is (a).

3

Final Answer

All show intersecting lines.

Key Points to Remember

Essential concepts to master this topic
  • Definition: Intersecting lines cross and meet at exactly one point
  • Identification: Look for lines that cross each other, not parallel arrangements
  • Verification: Check each figure has lines meeting at intersection points ✓

Common Mistakes

Avoid these frequent errors
  • Confusing intersecting lines with perpendicular lines
    Don't assume all intersecting lines are perpendicular = wrong classification! Intersecting lines can meet at any angle, not just 90°. Always focus on whether lines cross each other, regardless of the angle they form.

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

What's the difference between intersecting and perpendicular lines?

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Intersecting lines simply cross each other at any angle. Perpendicular lines are a special type of intersecting lines that meet at exactly 90° 90° angles.

Can parallel lines ever intersect?

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No! Parallel lines never meet or cross each other. They maintain the same distance apart forever. If lines intersect, they cannot be parallel.

Do all the figures show the same type of intersection?

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While all figures show intersecting lines, they don't all show the same angles. Some may be perpendicular (90°), others at different angles, but they all have the common property of crossing.

How do I identify intersecting lines in a diagram?

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Look for places where lines cross over each other. The key is finding the intersection point where two or more lines meet, regardless of the angle they form.

What if lines appear to intersect but don't actually touch?

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If lines don't actually touch or cross, they're not intersecting! They might be skew lines (in 3D) or simply separate lines that appear to cross due to perspective.

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