Determine whether the statement is true or false:
AD is the height of the triangle ADB.
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Determine whether the statement is true or false:
AD is the height of the triangle ADB.
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.
True,
Is DE side in one of the triangles?
Look for the right angle symbol (small square) where AD meets BD in the diagram. This symbol indicates a 90° angle, confirming perpendicularity.
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!
Yes! Every triangle has exactly three altitudes - one from each vertex to its opposite side. Each altitude is perpendicular to its corresponding base.
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!
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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