Identifying Perpendicular Lines: Analysis of a Quarter Circle Figure

Perpendicular Lines with Quarter Circle Figures

Are there two pairs of perpendicular lines in the figure?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Are there two perpendiculars in the drawing?
00:07 A perpendicular creates a right angle where two lines meet.
00:11 Let's mark and count all the right angles to find them.
00:16 And that's how we solve this question!

Step-by-step written solution

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1

Understand the problem

Are there two pairs of perpendicular lines in the figure?

2

Step-by-step solution

Remember that perpendicular lines form a 90-degree angle.

We will mark the intersection points of the lines with the letter T to work out if the angles are right angles, as follows:

From the drawing, it seems there are 2 right angles, which means there are indeed 2 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: Mark intersections with right angle squares to verify perpendicularity
  • Check: Count all right angle markers in the figure ✓

Common Mistakes

Avoid these frequent errors
  • Confusing intersecting lines with perpendicular lines
    Don't assume all intersecting lines are perpendicular = wrong identification! Lines can cross at any angle, not just 90°. Always verify that the intersection forms a perfect right angle before calling lines perpendicular.

Practice Quiz

Test your knowledge with interactive questions

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 really perpendicular just by looking?

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Look for right angle markers (small squares) at intersections! These squares indicate 90° angles. Without these markers, you need to measure or use geometric properties to verify perpendicularity.

Why does the quarter circle matter in this problem?

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The quarter circle helps form the figure, but the perpendicular relationships are between the straight lines only. Focus on where the straight lines intersect, not the curved part.

What exactly counts as 'two pairs' of perpendicular lines?

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A pair means two lines that are perpendicular to each other. So 'two pairs' means you need to find four different lines that form two separate perpendicular relationships.

Do I need to measure angles with a protractor?

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No! In geometry problems, right angle markers (small squares) tell you which angles are exactly 90°. Trust these visual indicators rather than trying to measure.

Can lines be perpendicular if they don't touch?

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Yes! Lines can be perpendicular even if they don't intersect within the visible figure. If you extend the lines, they would meet at a 90° angle.

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