Identifying Perpendicular Lines: Visual Geometry Analysis

Perpendicular Lines with Right Angle Recognition

Which of the following diagram shows perpendicular lines?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perpendiculars
00:03 A perpendicular is a line that forms a right angle at the intersection point with another line
00:07 Therefore all these lines are perpendicular
00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Which of the following diagram shows perpendicular lines?

2

Step-by-step solution

Remember that an angle is a straight line that forms a right angle of 90 degrees with another straight line.

In answer A, we can identify a right angle, therefore in diagram A there is an angle.

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines intersect at exactly 90 degrees
  • Visual Check: Look for the small square symbol at intersection
  • Verification: Both lines must be straight and form four equal angles ✓

Common Mistakes

Avoid these frequent errors
  • Confusing intersecting lines with perpendicular lines
    Don't assume any two lines that cross are perpendicular = wrong identification! Lines can intersect at many different angles (30°, 45°, 60°, etc.). Always check for the 90-degree right angle marker or square symbol at the intersection.

Practice Quiz

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Determine which lines are parallel to one another?

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 the small square symbol at the intersection point! This square indicates a 90-degree angle. Without this marker, you cannot assume lines are perpendicular even if they look like it.

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 intersect at exactly 90 degrees, while other intersecting lines can meet at any angle.

Can perpendicular lines be diagonal instead of horizontal and vertical?

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Absolutely! Perpendicular lines can point in any direction as long as they meet at a 90-degree angle. The key is the right angle, not whether they're horizontal or vertical.

Why is there a shaded square in the diagram?

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The shaded square is the right angle marker! It's a universal symbol in geometry that shows where two lines meet at exactly 90 degrees. This confirms the lines are perpendicular.

Do perpendicular lines have to be the same length?

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No! Perpendicular lines can be any length. What matters is that they intersect at a 90-degree angle, not their individual lengths.

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