Triangle Side Analysis: Is AB Perpendicular to BC in a Right-Angled Triangle?

Perpendicular Lines with Right Triangle Analysis

Is side AB perpendicular to side BC in the right-angled triangle below?

AAABBBCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is AB perpendicular to BC?
00:03 Perpendicular creates a right angle at the intersection point between the lines
00:06 We have a right angle between AB and BC, therefore they are perpendicular
00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is side AB perpendicular to side BC in the right-angled triangle below?

AAABBBCCC

2

Step-by-step solution

Remember that perpendicular lines are lines that form a 90-degree angle.

We will examine this by drawing the letter T at the intersection point of lines AB and BC as follows:

90°90°90°AAABBBCCCIt seems from the drawing that the angle formed between the lines is a right angle, therefore side AB is indeed perpendicular to side BC.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Perpendicular lines form exactly 90-degree angles at intersection
  • Visual Test: Draw a small square at point B to check for right angle
  • Verification: Confirm angle ABC measures exactly 90° using angle markers ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all triangle sides are perpendicular
    Don't think every side in a triangle is perpendicular to another = wrong geometric understanding! Only specific sides can be perpendicular based on the triangle's angles. Always check each angle individually - only sides forming a 90° angle are perpendicular.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

1234

FAQ

Everything you need to know about this question

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

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Look for a perfect right angle where the lines meet! You can use the 'T-test' - imagine drawing a capital letter T at the intersection. If it looks like a proper T with a 90° angle, the lines are perpendicular.

Are all sides in a right triangle perpendicular to each other?

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No! In a right triangle, only the two sides that form the right angle are perpendicular. The hypotenuse (longest side) is not perpendicular to the other two sides.

What's the difference between perpendicular and just intersecting lines?

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All perpendicular lines intersect, but not all intersecting lines are perpendicular! Perpendicular lines must form exactly 90° 90° angles. Other intersecting lines form acute or obtuse angles.

How do I mark a right angle in my drawing?

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Draw a small square symbol at the vertex where the two lines meet. This universally indicates a 90° angle. You can also write '90°' next to it for extra clarity.

Can I use a protractor to check if lines are perpendicular?

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Absolutely! Place the protractor's center at the intersection point and measure the angle. If it reads exactly 90°, the lines are perpendicular. This is the most accurate way to verify.

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