Counting Perpendicular Lines: Analyzing 12 Possible Line Pairs in a Geometric Figure

Perpendicular Lines with Right Angle Identification

The shape in the figure below contains only right angles.

Are there 12 pairs of perpendicular lines?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are there 12 perpendicular lines in the drawing?
00:04 A perpendicular creates a right angle at the intersection point between the lines
00:07 Let's mark and count all the right angles to find the perpendicular lines
00:23 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

The shape in the figure below contains only right angles.

Are there 12 pairs of perpendicular lines?

2

Step-by-step solution

Remember that perpendicular lines form a 90-degree angle.

We will mark on the figure all the right angles formed by the intersections of the lines as follows:

The figure shows that there are 12 right angles, therefore there are 12 pairs of perpendicular lines.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines meet at exactly 90-degree angles
  • Technique: Count right angle markers - each square symbol = one perpendicular pair
  • Check: Verify all 12 right angles are marked and counted correctly ✓

Common Mistakes

Avoid these frequent errors
  • Counting intersections instead of perpendicular pairs
    Don't count every line intersection as perpendicular = wrong answer! Some lines can cross without forming 90° angles. Always look for the small square markers that indicate right angles before counting.

Practice Quiz

Test your knowledge with interactive questions

Determine which lines are parallel to one another?

FAQ

Everything you need to know about this question

How can I tell if two lines are really perpendicular?

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Look for the small square symbol at the intersection point! This marker specifically shows a 90-degree angle. Without this symbol, you can't assume 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. Lines are only perpendicular when they meet at exactly 90 degrees.

Why does the problem ask about pairs of lines?

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Each right angle is formed by two lines meeting, so we count pairs. One right angle = one pair of perpendicular lines!

Can I just count the lines instead of the angles?

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No! You need to count the right angles (marked with squares), not just lines. Each right angle represents one pair of perpendicular lines.

What if I see more than 12 intersections in the figure?

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Remember, only intersections with right angle markers count as perpendicular pairs. Other intersections might be at different angles and don't count for this problem.

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