Identifying Perpendicular Lines: Visual Geometry Analysis with 4 Examples

Q: How can I tell if lines are perpendicular just by looking?

Look for right angle markers - small squares drawn at the intersection point. These squares indicate exactly 90 degrees. Also check if the lines form a perfect T-shape or cross where all four angles look equal.

Q: Why do some diagrams show small squares at intersections?

Those small squares are right angle symbols - they're the universal way to mark 90-degree angles in geometry. When you see this symbol, you know for certain the lines are perpendicular.

Q: Do perpendicular lines have to be horizontal and vertical?

Not at all! Perpendicular lines can be at any orientation - they just need to meet at 90 degrees. Think of an X shape tilted at 45 degrees - those lines are still perpendicular.

Q: In the example, why are drawings 1 and 2 both correct?

Both drawings show right angle markers (small squares) at their intersections. Drawing 1 shows vertical and horizontal lines, while drawing 2 shows lines at different angles, but both create perfect 90-degree intersections.

Perpendicular Lines with Visual Angle Recognition

Identify in which of the drawings the lines are perpendicular?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Which lines are perpendicular?

00:03 Perpendicular lines create a right angle at their intersection point

00:06 In this example, the lines form a right angle

00:13 In this example, the lines form an angle greater than 90

00:21 In this example, the lines form an angle greater than 90

00:29 In this example, the lines form a right angle

00:32 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Identify in which of the drawings the lines are perpendicular?

Step-by-step solution

Take note that perpendicular lines are lines that intersect at a 90-degree angle.

In order to better examine the types of angles that the lines create with one another, let's draw a T at the intersection point of the lines as follows:

Notice that from the drawings, in answers 1+2 a right angle is formed, meaning the lines in these drawings are perpendicular.

Final Answer

1 and 2

Key Points to Remember

Essential concepts to master this topic

Definition: Perpendicular lines intersect at exactly 90-degree angles
Technique: Draw small squares at intersections to check for right angles
Check: Look for perfect T-shapes or cross formations with equal quadrants ✓

Common Mistakes

Avoid these frequent errors

Assuming all intersecting lines are perpendicular
Don't think that any two lines crossing each other are perpendicular = wrong identification! Lines can intersect at many different angles (30°, 45°, 60°, etc.). Always check specifically for the 90-degree right angle marker or perfect square symbol at the intersection.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

FAQ

Everything you need to know about this question

How can I tell if lines are perpendicular just by looking?

Look for right angle markers - small squares drawn at the intersection point. These squares indicate exactly 90 degrees. Also check if the lines form a perfect T-shape or cross where all four angles look equal.

What's the difference between intersecting and perpendicular lines?

All perpendicular lines intersect, but not all intersecting lines are perpendicular! Intersecting just means the lines cross each other. Perpendicular means they cross at exactly $90°$ .

Can I use a protractor to check?

Yes! Place your protractor at the intersection point. If the angle measures exactly 90 degrees, the lines are perpendicular. This is especially helpful when the diagram doesn't show angle markers.

Why do some diagrams show small squares at intersections?

Those small squares are right angle symbols - they're the universal way to mark 90-degree angles in geometry. When you see this symbol, you know for certain the lines are perpendicular.

Do perpendicular lines have to be horizontal and vertical?

Not at all! Perpendicular lines can be at any orientation - they just need to meet at 90 degrees. Think of an X shape tilted at 45 degrees - those lines are still perpendicular.

In the example, why are drawings 1 and 2 both correct?

Both drawings show right angle markers (small squares) at their intersections. Drawing 1 shows vertical and horizontal lines, while drawing 2 shows lines at different angles, but both create perfect 90-degree intersections.

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