Triangle ABC: Identifying the Correct Height Line

Triangle Heights with Perpendicular Line Segments

Which of the following is the height in triangle ABC?

AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the height of the triangle
00:03 The height in a triangle is a perpendicular line from a vertex to the opposite side
00:07 At the intersection point, the angle between the lines is a right angle
00:21 In a right triangle, the 2 legs can be considered as heights
00:24 This is the solution

Step-by-step written solution

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1

Understand the problem

Which of the following is the height in triangle ABC?

AAABBBCCCDDD

2

Step-by-step solution

Let's remember the definition of height of a triangle:

A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.

The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.

3

Final Answer

AB

Key Points to Remember

Essential concepts to master this topic
  • Definition: Height is a line from vertex perpendicular to opposite side
  • Technique: Look for 90° angle symbol shown as small square
  • Check: Height must connect vertex to opposite side forming right angle ✓

Common Mistakes

Avoid these frequent errors
  • Confusing height with any side of the triangle
    Don't assume any side like AC or BC is automatically the height = wrong identification! A height must be perpendicular to a side, not just connect two vertices. Always look for the line that forms a 90-degree angle with the base.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

How do I know which line is the height?

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Look for the right angle symbol (small square) where a line meets a side! The height is the line segment that forms this 90° angle with the opposite side.

Can any side of a triangle be a height?

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Only in special cases! In a right triangle, the two sides that form the right angle can serve as heights to each other. But usually, heights are separate line segments drawn perpendicular to the sides.

Why isn't AC or BC the height in this triangle?

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AC and BC are sides of the triangle, not heights. A height must be perpendicular to a side. In this diagram, AB is perpendicular to BC, making AB the height.

What if I can't see the right angle symbol clearly?

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Look for visual clues like the line appearing to form a perfect corner with the base. Heights are always drawn at exactly 90 degrees, making them look like they form square corners.

Can a triangle have more than one height?

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Yes! Every triangle has three heights - one from each vertex to the opposite side. But in any given problem, you're usually asked to identify one specific height.

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