Geometric Analysis: Determining Perpendicular Line Relationships

Perpendicular Lines with Right Angle Identification

Which lines are perpendicular to each other?

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Step-by-step video solution

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00:00 Which of the lines are perpendicular to each other?
00:02 Perpendicular lines create a right angle at their intersection point
00:05 In this example, the angle between the lines is unknown
00:08 In this example, the lines never intersect and therefore are parallel
00:14 In this example, the lines form a right angle therefore they are perpendicular
00:21 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Which lines are perpendicular to each other?

2

Step-by-step solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where the lines form a right angle of 90 degrees between them is drawing A.

3

Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines form exactly 90-degree right angles when intersecting
  • Visual Check: Look for square corner symbols at intersection points
  • Verification: Measure angle with protractor: must equal exactly 90° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming any intersecting lines are perpendicular
    Don't think all crossing lines are perpendicular = wrong identification! Most intersecting lines form acute or obtuse angles, not 90°. Always look for the small square symbol or verify the angle measures exactly 90 degrees.

Practice Quiz

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The lines below are not the same size, but are they parallel?

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 indicates a right angle. The lines should also appear to form four equal angles that look like perfect corners.

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 are a special case where the intersection creates exactly 90° angles.

Can diagonal lines be perpendicular to each other?

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Absolutely! Lines don't have to be horizontal and vertical to be perpendicular. As long as they meet at a 90° angle, any two lines can be perpendicular, regardless of their orientation.

Why do some diagrams show small squares at intersections?

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Those small squares are right angle markers - they're mathematical symbols that tell you the angle is exactly 90°. Without this symbol, you can't assume lines are perpendicular!

Are parallel lines ever perpendicular?

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No! Parallel lines never intersect, so they can't form any angle at all. Perpendicular lines must cross each other to create the 90° angle.

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