Identifying Perpendicular Lines: 90-Degree Angle Recognition

Angle Recognition with Visual Intersection Analysis

Which of the diagrams shows perpendicular lines?

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Step-by-step video solution

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00:00 Which of the lines are perpendicular?
00:03 Perpendicular lines form a right angle at their intersection point
00:08 In this example, the lines form an angle less than 90°
00:11 In this example, the lines form a right angle
00:16 In this example, the lines form an angle less than 90°
00:22 In this example, the lines form an angle less than 90°
00:26 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Which of the diagrams shows perpendicular lines?

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Step-by-step solution

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

To check if the lines form a 90-degree angle, for each of the drawings a T is drawn at the intersecting point of the lines.

Let's examine figure A:

Note that the lines do not form a right angle.

Let's examine figure B:

We notice that the lines form a 90-degree angle and therefore are perpendicular.

Let's examine figure C:

Note that the lines do not form a right angle.

Let's examine figure D:

Note that the lines do not form a right angle.

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Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines intersect forming exactly 90-degree angles
  • Visual Check: Draw T-shape at intersection; square corner indicates perpendicular
  • Verification: Test all four angles formed; each measures 90° ✓

Common Mistakes

Avoid these frequent errors
  • Assuming lines are perpendicular without measuring angles
    Don't assume intersecting lines are perpendicular just because they cross = wrong identification! Lines can intersect at any angle from 0° to 180°, not just 90°. Always check if the angle formed is exactly a right angle by drawing a T-test or using angle markers.

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 without a protractor?

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Use the T-test method! Draw a small T-shape at the intersection point. If the horizontal line of the T fits perfectly between the two lines without gaps or overlaps, they're perpendicular.

Do perpendicular lines always look like a plus sign?

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Not always! While a + shape shows perpendicular lines, they can also form an upside-down T, sideways T, or rotated cross. The key is the 90-degree angle, not the orientation.

What's the difference between intersecting and perpendicular lines?

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All perpendicular lines intersect, but not all intersecting lines are perpendicular! Intersecting just means they cross somewhere. Perpendicular means they cross at exactly 90 degrees.

Can I have perpendicular lines that don't touch?

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No! By definition, perpendicular lines must intersect (touch) at exactly one point. If lines don't intersect, they're either parallel or skew, never perpendicular.

Why does the square symbol appear in some diagrams?

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The small square symbol at an intersection is the universal mark for a right angle (90°). It's a quick visual way to show that two lines are perpendicular without measuring.

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