Identifying Perpendicular Lines: 90-Degree Angle Analysis

Perpendicular Lines with Visual Angle Analysis

Which of these lines are perpendicular to each other?

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Step-by-step video solution

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00:03 Which of the lines are perpendicular?
00:07 Remember! Perpendicular lines meet to form a right angle, which is 90 degrees.
00:14 In this example, the lines create an angle that's greater than 90 degrees.
00:31 Here, the lines create an angle that's less than 90 degrees.
00:38 In this example, the lines meet at a perfect right angle, exactly 90 degrees!
00:47 Once again, the lines make an angle greater than 90 degrees.
00:52 And that's how we find the perpendicular lines. Great job!

Step-by-step written solution

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Understand the problem

Which of these lines are perpendicular to each other?

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Step-by-step solution

Let's remember that perpendicular lines form a 90-degree angle.

In each of the answers, we will draw the letter T at the intersection point of the lines.

Let's examine figure A:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure B:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure C:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure D:

We notice that the lines do form a right angle therefore are perpendicular lines.

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Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines always intersect at exactly 90 degrees
  • Technique: Draw small square at intersection to verify right angle
  • Check: Lines forming perfect L-shape or T-shape are perpendicular ✓

Common Mistakes

Avoid these frequent errors
  • Assuming lines that cross are automatically perpendicular
    Don't assume any two intersecting lines are perpendicular = wrong identification! Lines can cross at many different angles. Always check that the intersection angle measures exactly 90 degrees by looking for the square corner symbol.

Practice Quiz

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What do the four figures below have in common?

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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 lines that form an L-shape or T-shape. One line should be perfectly horizontal and the other perfectly vertical, or they should meet at what looks like a perfect square corner.

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 angle is exactly 90° 90° .

Why do some figures show a small square at the intersection?

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The small square is the right angle symbol! It's mathematical notation that confirms the angle measures exactly 90° 90° . This symbol makes it easy to identify perpendicular lines.

Can perpendicular lines be diagonal?

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Yes! Perpendicular lines don't have to be horizontal and vertical. They just need to meet at a 90° 90° angle. Think of an X rotated 45 degrees - those lines are still perpendicular.

What if the lines don't look exactly perpendicular in the drawing?

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Always look for the right angle symbol (small square) rather than relying on visual estimation. Drawings might not be perfectly to scale, but the mathematical symbols are accurate.

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