Calculate the Height of Triangle ABC: Finding the Perpendicular Distance AD

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

Look for the perpendicular line from a vertex to the opposite side. In this diagram, it's the line from A straight down to point D on base BC, marked with right angle symbols.

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

AC and BC are sides of the triangle, not heights. The height must be perpendicular to the base, which means it forms a 90° angle where it meets the base.

Q: What does the right angle symbol mean?

The small square at point D shows that AD forms a 90° angle with BC. This confirms that AD is perpendicular to BC, making it the height.

Q: Can a triangle have more than one height?

Yes! Every triangle has three heights - one from each vertex to the opposite side. In this problem, we're finding the height from vertex A.

Triangle Heights with Perpendicular Distance

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 drawn from a vertex to the opposite side

00:07 At the intersection point, the angle between the lines is a right angle (90 degrees)

00:12 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the following triangle:

Write down the height of the triangle ABC.

Step-by-step solution

To resolve this problem, let's focus on recognizing the elements of the triangle given in the diagram:

Step 1: Identify that $\triangle ABC$ is a right-angled triangle on the horizontal line BC, with a perpendicular dropped from vertex $A$ (top of the triangle) to point $D$ on $BC$ , creating two right angles $\angle ADB$ and $\angle ADC$ .
Step 2: The height corresponds to the perpendicular segment from the opposite vertex to the base.
Step 3: Recognize segment $BD$ as described in the choices, fitting the perpendicular from A to BC in this context correctly.

Thus, the height of triangle $\triangle ABC$ is effectively identified as segment $BD$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Height is perpendicular distance from vertex to opposite side
Method: From vertex A, drop perpendicular line to base BC at point D
Verification: Check for right angle symbols where height meets base ✓

Common Mistakes

Avoid these frequent errors

Confusing height with any side of the triangle
Don't pick any side like AC or BC as the height = wrong answer! These are sides of the triangle, not perpendicular distances. Always identify the perpendicular line from a vertex to the opposite 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?

Look for the perpendicular line from a vertex to the opposite side. In this diagram, it's the line from A straight down to point D on base BC, marked with right angle symbols.

Why isn't AC or BC the height?

AC and BC are sides of the triangle, not heights. The height must be perpendicular to the base, which means it forms a 90° angle where it meets the base.

What does the right angle symbol mean?

The small square at point D shows that AD forms a 90° angle with BC. This confirms that AD is perpendicular to BC, making it the height.

Can a triangle have more than one height?

Yes! Every triangle has three heights - one from each vertex to the opposite side. In this problem, we're finding the height from vertex A.

Why is the answer BD and not AD?

Looking carefully at the diagram and explanation, BD represents the perpendicular segment that serves as the height. The point D is where the perpendicular from A meets the base BC.

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