Geometric Analysis: Identifying Intersecting Lines in Multiple Diagrams

Line Relationships with Intersection Analysis

Which figure(s) show intersecting lines?

1234

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Which lines cross each other?
00:06 When lines intersect, they split each other into two equal parts.
00:11 In this example, the lines intersect. Why? Because the segments are equal.
00:17 Here, the lines form a right angle. So, they are perpendicular.
00:21 But if segments aren't equal, they don't intersect.
00:26 In this case, the lines never meet, making them parallel.
00:31 Here, the lines intersect because the segments are equal.
00:35 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which figure(s) show intersecting lines?

1234

2

Step-by-step solution

Lines that intersect each other are lines that meet or cross each other.

The diagrams showing lines that cross each other are 1 and 3.

In diagram 2, the lines are perpendicular and vertical to each other, while in drawing 4, the lines are parallel to each other.

3

Final Answer

1 and 3

Key Points to Remember

Essential concepts to master this topic
  • Intersection Definition: Lines that meet or cross at a point
  • Visual Analysis: Look for X-patterns or crossing shapes in diagrams
  • Verification: Count crossing points - intersecting lines create one meeting point ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perpendicular lines with intersecting lines
    Don't assume all perpendicular lines intersect = wrong identification! Perpendicular lines can be separate and never meet. Always check if the lines actually cross or meet at a point.

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 parallel lines?

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Intersecting lines meet or cross each other at one point, while parallel lines never meet - they stay the same distance apart forever, like railroad tracks.

Can perpendicular lines also be intersecting lines?

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Yes! Perpendicular lines are a special type of intersecting lines that meet at exactly 90° angles. But not all intersecting lines are perpendicular - they can cross at any angle.

How do I identify intersecting lines in a diagram?

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Look for lines that cross each other or meet at a point. You'll see an X-shape, T-shape, or plus sign (+) pattern where the lines come together.

In this problem, why aren't figures 2 and 4 showing intersecting lines?

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Figure 2 shows perpendicular lines that don't actually meet - they form a cross pattern but are separate. Figure 4 shows parallel lines that never cross each other.

What if lines look like they almost intersect?

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Almost doesn't count! Lines either intersect (meet at a point) or they don't. If they're very close but don't actually touch, they're not intersecting.

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