Triangle Height Verification: Is AD the Altitude of Triangle ABD?

Triangle Altitude with Perpendicular Verification

Determine whether the statement is true or false:

AD is the height of the triangle ADB.

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Step-by-step written solution

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1

Understand the problem

Determine whether the statement is true or false:

AD is the height of the triangle ADB.

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2

Step-by-step solution

To determine whether AD is the height of triangle ADB, we must inspect whether segment AD is perpendicular to the base BD. By definition, the height of a triangle from a vertex is a line segment perpendicular to the line containing the opposite side. The diagram describes that AD is a vertical line, indicating a perpendicular relationship to the horizontal line BC. Thus, within triangle ADB, AD perfectly aligns as the height from vertex A to the base BD.

Therefore, the statement is True.

3

Final Answer

True,

Key Points to Remember

Essential concepts to master this topic
  • Definition: Altitude is a perpendicular line from vertex to opposite side
  • Visual Check: Look for right angle symbol where AD meets BD
  • Verification: Confirm AD forms 90° angle with base BD ✓

Common Mistakes

Avoid these frequent errors
  • Confusing any line from vertex as altitude
    Don't assume any line from A to side BD is automatically the altitude = wrong identification! A line is only an altitude if it's perpendicular to the opposite side. Always check for the right angle marker or perpendicular relationship.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?
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FAQ

Everything you need to know about this question

How can I tell if AD is really perpendicular to BD?

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Look for the right angle symbol (small square) where AD meets BD in the diagram. This symbol indicates a 90° angle, confirming perpendicularity.

What's the difference between altitude and just any line segment?

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An altitude must be perpendicular to the opposite side, while any other line segment from a vertex might be at a different angle. Only perpendicular lines qualify as altitudes!

Can a triangle have more than one altitude?

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Yes! Every triangle has exactly three altitudes - one from each vertex to its opposite side. Each altitude is perpendicular to its corresponding base.

What if the altitude falls outside the triangle?

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In obtuse triangles, some altitudes extend outside the triangle to meet the extended base line. They're still altitudes as long as they're perpendicular!

Why does the diagram show AD as a vertical line?

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The vertical position makes it easy to see that AD is perpendicular to the horizontal base BD. Vertical and horizontal lines always meet at right angles.

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