Calculate the Height of Triangle ABC: Perpendicular Altitude Construction

Triangle Height with Perpendicular Altitude

Given the following triangle:

Write down the height of the 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
00:11 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCDDD

2

Step-by-step solution

To determine the height of triangle ABC \triangle ABC , we need to identify the line segment that extends from a vertex and meets the opposite side at a right angle.

Given the diagram of the triangle, we consider the base AC AC and need to find the line segment from vertex B B to this base.

From the diagram, segment BD BD is drawn from B B and intersects the line AC AC (or its extension) perpendicularly. Therefore, it represents the height of the triangle ABC \triangle ABC .

Thus, the height of ABC \triangle ABC is segment BD BD .

3

Final Answer

BD

Key Points to Remember

Essential concepts to master this topic
  • Height Definition: Line segment perpendicular from vertex to opposite side
  • Identification: Look for right angle markers where segment meets base
  • Verification: Height must form 90° angle with base line ✓

Common Mistakes

Avoid these frequent errors
  • Confusing height with any side of the triangle
    Don't choose sides AC, BC, or AB as the height = wrong answer! These are sides of the triangle, not heights. Always look for the perpendicular line segment from a vertex to the opposite side.

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

What makes BD the height instead of just another line?

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BD is the height because it's perpendicular to the base AC. Look for the small square symbol in the diagram - this shows the 90-degree angle that makes BD a true height!

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. In this problem, BD is the height from vertex B to base AC.

Does the height always land inside the triangle?

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Not always! In obtuse triangles, some heights fall outside the triangle on the extended base line. The height is still measured as the perpendicular distance.

How do I spot the height in a diagram?

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Look for these clues:

  • A line from a vertex to the opposite side
  • Small square symbols showing right angles
  • The line appears perpendicular to the base

Why isn't AD the height?

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AD goes from vertex A, but we need the height to the base AC. Since A is already on the base AC, AD cannot be perpendicular to AC - it would just be part of the base!

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