Calculate Triangle Height: Finding Altitude AD in Triangle ABC

Q: How do I know which line is the height?

Look for the right angle symbol (small square) where the line meets the base. In this diagram, $ AD $ has a right angle symbol at point $ D $, showing it's perpendicular to base $ BC $.

Q: Why isn't AB or AC the height?

Because $ AB $ and $ AC $ are the sides of the triangle, not heights. Heights must be perpendicular to the opposite side, while triangle sides are slanted.

Q: Can a triangle have more than one height?

Yes! Every triangle has three heights - one from each vertex to the opposite side. This problem asks specifically for the height from vertex $ A $.

Q: What if the height falls outside the triangle?

In obtuse triangles, some heights can fall outside the triangle. But you still measure the perpendicular distance from the vertex to the extended base line.

Q: Is the height always vertical?

No! The height is perpendicular to the base, not necessarily vertical. If the base is tilted, the height will be tilted too, but still forms a 90° angle with the base.

Triangle Heights with Perpendicular Altitude

Given the following triangle:

Write down the height of the triangle ABC.

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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

00:06 or to the extension of the side

00:09 At the intersection point, the angle between the lines is a right angle (90 degrees)

00:14 This is the solution

Step-by-step written solution

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Understand the problem

Given the following triangle:

Write down the height of the triangle ABC.

Step-by-step solution

To solve this problem, we need to identify the height of triangle ABC from the diagram. The height of a triangle is defined as the perpendicular line segment from a vertex to the opposite side, or to the line containing the opposite side.

In the given diagram:

$A$ is the vertex from which the height is drawn.
The base $BC$ is a horizontal line lying on the same level.
$AD$ is the line segment originating from point $A$ and is perpendicular to $BC$ .

The perpendicularity of $AD$ to $BC$ is illustrated by the right angle symbol at point $D$ . This establishes $AD$ as the height of the triangle ABC.

Considering the options provided, the line segment that represents the height of the triangle ABC is indeed $AD$ .

Therefore, the correct choice is: $AD$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Height is perpendicular segment from vertex to opposite side
Identification: Look for right angle symbol (square) at base
Verification: Height forms 90° angle with base line ✓

Common Mistakes

Avoid these frequent errors

Confusing height with triangle sides
Don't choose any side like AB or AC as the height = selecting slanted lines! These are sides of the triangle, not perpendicular distances. Always identify the perpendicular line segment marked with a right angle symbol.

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?

Look for the right angle symbol (small square) where the line meets the base. In this diagram, $AD$ has a right angle symbol at point $D$ , showing it's perpendicular to base $BC$ .

Why isn't AB or AC the height?

Because $AB$ and $AC$ are the sides of the triangle, not heights. Heights must be perpendicular to the opposite side, while triangle sides are slanted.

Can a triangle have more than one height?

Yes! Every triangle has three heights - one from each vertex to the opposite side. This problem asks specifically for the height from vertex $A$ .

What if the height falls outside the triangle?

In obtuse triangles, some heights can fall outside the triangle. But you still measure the perpendicular distance from the vertex to the extended base line.

Is the height always vertical?

No! The height is perpendicular to the base, not necessarily vertical. If the base is tilted, the height will be tilted too, but still forms a 90° angle with the base.

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