Calculate the Height of Triangle ABC: Perpendicular Distance Problem

Q: What makes AE the correct height instead of AC or AB?

The altitude (height) must be perpendicular to the base! AE forms a 90° angle with base BC, shown by the square symbol. AC and AB are just sides of the triangle.

Q: How can I identify the altitude in any triangle diagram?

Look for these clues: A perpendicular symbol (small square) where the line meets the baseA dashed or different colored line from vertex to opposite sideThe line forms a 90° angle with the base

Q: Why isn't AD the altitude?

AD connects point A to point D on side BC, but it's not perpendicular to BC. The altitude must form a right angle with the base, which only AE does in this diagram.

Q: Can a triangle have more than one altitude?

Yes! Every triangle has three altitudes - one from each vertex to the opposite side. In this problem, we're specifically looking for the altitude from vertex A.

Q: What if the altitude falls outside the triangle?

In obtuse triangles, some altitudes can fall outside the triangle. You'd extend the base line and draw the perpendicular from the vertex to meet this extended line.

Triangle Altitudes with Perpendicular Height Identification

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:

00:08 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

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Understand the problem

Given the following triangle:

Write down the height of the triangle ABC.

Step-by-step solution

An altitude in a triangle is the segment that connects the vertex and the opposite side, in such a way that the segment forms a 90-degree angle with the side.

If we look at the image it is clear that the above theorem is true for the line AE. AE not only connects the A vertex with the opposite side. It also crosses BC forming a 90-degree angle. Undoubtedly making AE the altitude.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Altitude connects vertex to opposite side forming 90° angle
Identification: Look for perpendicular symbol (square) where segment meets base
Verification: Check that AE connects vertex A to base BC perpendicularly ✓

Common Mistakes

Avoid these frequent errors

Confusing altitude with any side of the triangle
Don't choose sides like AC or AB as the height = wrong answer! These are just sides of the triangle, not perpendicular distances. Always look for the segment that forms a 90° angle with the base.

Practice Quiz

Test your knowledge with interactive questions

Can a triangle have a right angle?

FAQ

Everything you need to know about this question

What makes AE the correct height instead of AC or AB?

The altitude (height) must be perpendicular to the base! AE forms a 90° angle with base BC, shown by the square symbol. AC and AB are just sides of the triangle.

How can I identify the altitude in any triangle diagram?

Look for these clues:

A perpendicular symbol (small square) where the line meets the base
A dashed or different colored line from vertex to opposite side
The line forms a 90° angle with the base

Why isn't AD the altitude?

AD connects point A to point D on side BC, but it's not perpendicular to BC. The altitude must form a right angle with the base, which only AE does in this diagram.

Can a triangle have more than one altitude?

Yes! Every triangle has three altitudes - one from each vertex to the opposite side. In this problem, we're specifically looking for the altitude from vertex A.

What if the altitude falls outside the triangle?

In obtuse triangles, some altitudes can fall outside the triangle. You'd extend the base line and draw the perpendicular from the vertex to meet this extended line.

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